Terrell's company sells candy in packs that are supposed to contain 50% red candies, 25% orange, and 25% yellow. He randomly selected a pack containing 16 candies and counted how many of each color were in the pack. Here are his results: Color Red Orange Yellow Observed counts 9 5 2 He wants to use these results to carry out a x2 goodness-of-fit test to determine if the color distribution disagrees with the target percentages. Which count(s) make this sample fail the large counts condition for this test? Choose 2 answers: A The observed count of yellow candies. B The observed count of orange candies

Answer:

44 ÷ 2,876 = 0.01528 (rounded to five decimal places)

Step-by-step explanation:

To divide 44 by 2,876, we can use long division. Here are the steps:

Write 44 under the long division symbol (÷) and 2,876 outside the symbol.

      ___

   2,876 | 44

Since 2 is smaller than 44, we can't divide 2,876 by 44, so we need to add a decimal point and a zero to the quotient and bring down the next digit of the dividend (4).

      ___

   2,876 | 44.0

      ___

   2,876 | 44.0

               4

We see that 28 is the largest multiple of 2,876 that is less than or equal to 440. We write 28 above the line, and multiply 2,876 by 28 to get 80,528. We subtract 80,528 from 440, which gives us a remainder of 4.

       28

      ___

   2,876 | 44.0

              4 4 0

         -    3 4 2 8

              -------

                8 4

Since we have a remainder of 4, we can't bring down any more digits from the dividend, so we add a decimal point and a zero to the quotient and bring down a zero to make the dividend 40. We repeat the process of finding the largest multiple of 2,876 that is less than or equal to 400, writing it above the line, multiplying it by 2,876, subtracting the result from the dividend, and bringing down the next digit.

       28. 0

      ___

   2,876 | 44.0

          4 4 0

        - 3 4 2 8

             -------

            8 4

            8 3 6

          - 8 0 4

             -------

              3 2

We have a remainder of 32, and we can't bring down any more digits from the dividend, so we add a decimal point and a zero to the quotient and bring down another zero to make the dividend 320. We repeat the process of finding the largest multiple of 2,876 that is less than or equal to 3,200, writing it above the line, multiplying it by 2,876, subtracting the result from the dividend, and bringing down the next digit.

       28. 00

      ___

   2,876 | 44.0

               4 4 0

             - 3 4 2 8

               -------

               8 4

               8 3 6

             - 8 0 4

              -------

              3 2

              2 8 2

            - 2 8 7 6

            -------

                  6

We have a remainder of 6, and we can't bring down any more digits from the dividend, so we have our final answer:

44 ÷ 2,876 = 0.01528 (rounded to five decimal places)

½ of a 12 inches pizza represents the bigger portion.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

½ of a 12-inch pizza, then the area is given as,

A = (π / 2) x (12 / 2)²

A = 56.52 square inches

30% of a 9-inch pizza. Then the area is given as,

A = 0.30 x π (9 / 2)²

A = 19.0755 square inches

½ of a 12 inches pizza represents the bigger portion.

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In 15 years the investment will be worth $586.99.

Compound interest is the addition of interest to the principal sum of a loan or deposit or interest on interest plus interest.

It is the result of reinvesting interest, or adding it to the loaned capital, rather than paying it out or requiring payment from the borrower, so that interest is earned on the principal sum plus previously accumulated interest in the following period.

In finance and economics, compound interest is the norm.

To find how much will the investment be worth in 20 years:

Given -

Initial investment = $300.

Interest rate = 4.5%.

Interest applied = quarterly.

So, the table of 15 years will be as follows:

using the formula we get,

Therefore, in 15 years the investment will be worth $586.99

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9x² + 14x +1 is the sum of polynomials 9x² + 5x + 8 and 9x – 7.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

We need to find the sum of  9x² + 5x + 8 and 9x – 7.

Summation is the addition of a sequence of any kind of numbers.

So add  9x² + 5x + 8 and 9x – 7.

9x² + 5x + 8 + 9x – 7.

Add the like terms

9x² + 14x +1

Hence, 9x² + 14x +1 is the sum of polynomials 9x² + 5x + 8 and 9x – 7.

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All the sample tests are stated below:

1) A two-independent-sample t test.

2) A one-sample t test.

3) A related-samples t test.

4)  A related-samples t test.

It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing. A sample must be representative of the entire population and must not be biased toward any one trait.

A professor runs an experiment to see if front-row students perform better on an exam than back-row pupils.

This is a two-independent-sample t test, as there are two distinct groups (students in the front row and students in the back row) and the professor is interested in comparing the mean exam scores between them.

To determine whether students spend more than 30 minutes on an activity on average, a graduate student chooses a sample of 25 participants.

This is a one-sample t test, as there is only one group of participants and the graduate student is interested in comparing the mean time students attend to a task to a specific value (30 minutes).

To determine whether right-handed siblings exhibit higher emotional intelligence than left-handed siblings, a researcher pairs up right- and left-handed siblings.

This is a related-samples t test using a matched-pairs design, as the researcher is interested in comparing emotional intelligence scores of right-handed and left-handed siblings who are matched based on certain criteria (in this case, being siblings).

A local school's principal is curious to discover how much an honors class benefits the children there. He administers tests to honors English students before the start of the school year and again at the conclusion of the year to gauge their progress.

This is a related-samples t test using a repeated-measures design, as the principal is interested in comparing the test scores of the same group of students before and after taking the honors English class to measure how much they learned during the year.

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Answer: The height is 3.5 cubic feet

Step-by-step explanation:

We have to find the area of the base first so multiply 25 and 18 feet together. You will get 450

Now you can make an equation.

525 = (1/3)*450*h

Multiply the 1/3 and the 450 together to get 150

Your equation is now 525 = 150h

Divide 150 on both sides to isolate h

You now have 3.5 = h

a) The probability that an individual overhead reach distance is greater than 218.40 cm is about 0.0594.

b) The probability that the mean for 20 randomly selected overhead reach distances is greater than 203.20 cm is about 0.7930.

c) The central limit theorem applies and we can use the normal distribution to approximate the sampling distribution of the sample means.

Probability is a way to evaluate how likely something is to happen. Several things are difficult to forecast with absolute confidence.

Now in the given question ,

a. To find the probability that an individual distance is greater than 218.40 cm, we can use the z-score formula:

z = (x - μ) / σ

where x is the individual distance, μ is the mean overhead reach distance, and σ is the standard deviation of the overhead reach distances. Plugging in the values given, we have:

z = (218.40 - 205) / 8.6

z = 1.56

Using a standard normal table or calculator, we can find the probability that a z-score is greater than 1.56 to be approximately 0.0594. Therefore, the probability that an individual overhead reach distance is greater than 218.40 cm is about 0.0594.

b. To find the probability that the mean for 20 randomly selected distances is greater than 203.20 cm, we need to use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normal, with a mean of μ and a standard deviation of σ / sqrt(n), where n is the sample size. In this case, we have:

μ = 205

σ = 8.6

n = 20

So the standard deviation of the sample means is:

σ / sqrt(n) = 8.6 / sqrt(20) = 1.923

Next, we need to find the z-score corresponding to a mean of 203.20 cm:

z = (203.20 - 205) / 1.923

z = -0.82

Using a standard normal table or calculator, we can find the probability that a z-score is greater than -0.82 to be approximately 0.7930. Therefore, the probability that the mean for 20 randomly selected overhead reach distances is greater than 203.20 cm is about 0.7930.

c. The normal distribution can be used in part (b) because of the central limit theorem. Even though the sample size is less than 30, the sampling distribution of the sample means will still be approximately normal if the population distribution is normal or if the sample size is large enough. In this case, we are told that the population distribution of overhead reach distances is normal, so the central limit theorem applies and we can use the normal distribution to approximate the sampling distribution of the sample means.

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With given percentages of taxes on income, Alex and Tory owe $18,882 in federal taxes.

what exactly is a percentage?

A percentage is a way of representing a number as a fraction of 100. It is often denoted by "%". For example, 50% means 50 out of 100, or 0.5 as a decimal. Percentages are commonly used to express rates, ratios, and proportions in many areas such as finance, statistics, and everyday life.

Now,

Since the couple is married and filing jointly, their standard deduction is $25,900. Thus, their taxable income is $150,000 - $25,900 = $124,100.

From the tax table, the tax on the first $19,750 is 10% and the tax on the next $60,500 ($80,250 - $19,750) is 12%. The remaining taxable income is $124,100 - $80,250 = $43,850, which falls into the 22% tax bracket.

Therefore, the tax owed on the first $19,750 is $1,975 (10% of $19,750), the tax owed on the next $60,500 is $7,260 ($1,975 plus 12% of $60,500 - $19,750), and the tax owed on the remaining $43,850 is $9,647 (22% of $43,850).

The total tax owed is the sum of these amounts: $1,975 + $7,260 + $9,647 = $18,882. Therefore, Alex and Tory owe $18,882 in federal taxes.

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The margin of error to compare all pairs of means with Bonferroni's procedure with 94% family confidence are [9.17, 20.17], [-4.66, 6.34] and  [37.17, 48.17]. The margin of error for the difference in means between Samoas and Tagalongs is approximately 14.97.

To compute the margin of error to compare all pairs of means with Bonferroni's procedure with 94% family confidence, we need to use the formula:

Margin of error = t* (Sqrt (MSE/n))

Where t* is the critical value for a two-tailed t-test with a significance level of alpha = (1 - 0.94)/2 = 0.03,

degrees of freedom (df) = N - k,

where N is the total sample size (N = n * k = 8 * 4 = 32)

and k is the number of groups (k = 4), and MSE is the mean square error from the analysis of variance (ANOVA).

To find the critical value t* from the t-distribution table or calculator,

we need to look up the value of t for alpha/2 = 0.03/2 = 0.015 and df = 32 - 4 = 28, which is approximately 2.5.

The mean square error MSE is calculated by dividing the residual sum of squares (SSR) by the degrees of freedom within (dfw), which is

N - k = 32 - 4 = 28.

From the ANOVA table, we have:

SSR = 3458.08

dfw = 28

MSE = SSR/dfw = 3458.08/28 = 123.50

Now we can compute the margin of error for each pair of means with a 94% family confidence level, which means that the overall family

error rate is alpha = 1 - 0.94 = 0.06, and

the individual error rate for each comparison is alpha/k(k-1)/2 = 0.06/6 = 0.01.

For Do-si-dos vs. Samoas, the difference in means is 23 - 8.33 = 14.67. The margin of error is:

t* (Sqrt (MSE/n)) = 2.5 * (Sqrt (123.50/8)) = 5.50

The 94% family confidence interval for this comparison is [14.67 - 5.50, 14.67 + 5.50] = [9.17, 20.17].

For Do-si-dos vs. Tagalongs, the difference in means is 9.17 - 8.33 = 0.84. The margin of error is:

t* (Sqrt (MSE/n)) = 2.5 * (Sqrt (123.50/8)) = 5.50

The 94% family confidence interval for this comparison is [0.84 - 5.50, 0.84 + 5.50] = [-4.66, 6.34].

For Do-si-dos vs. Thin Mints, the difference in means is 51 - 8.33 = 42.67. The margin of error is:

t* (Sqrt (MSE/n)) = 2.5 * (Sqrt (123.50/8)) = 5.50

The 94% family confidence interval for this comparison is [42.67 - 5.50, 42.67 + 5.50] = [37.17, 48.17].

For Samoas vs. Tagalongs, the difference in means is 9.17 - 23 = -13.83. The Margin of error = 2.326 * 11.02 * √(1/8 + 1/8) ≈ 14.97

Therefore, the margin of error for the difference in means between Samoas and Tagalongs is approximately 14.97.

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Answer:

Below

Step-by-step explanation:

Answer C

The water station would be located at 2.92 miles. Round to the nearest tenth of a mile, the answer is 2.9 miles.

Distance is a numerical value that quantifies "how much ground an object has traveled" while in motion. Distance is calculated as the sum of a person's movement and time.

Call the distance between the starting point and the water station x. 5 - x meters separate from the water station from the finish line.

We may write the following equation because we are aware that the ratio between these two lengths is 7:5.

x / (5 - x) = 7/5

Expanding and solving for x, we get:

5x = 7(5) - 7x

12x = 35

x = 35/12 = 2.92 miles

Therefore, the distance of the water station would be 2.9 miles.

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Answer:

Below

Step-by-step explanation:

For this , I will assume  i = [tex]\sqrt{-1}[/tex]

i^{11} + i^{16} + i^{21} + i^{26} + i^{31}  =

-  i         +1        +i            -1        - i       =     - i  

Answer:

[tex]\textsf{Increasing}: \quad (- \infty, -1) \cup (1, \infty)[/tex]

[tex]\textsf{Decreasing}: \quad(-1, 1)[/tex]

[tex]\textsf{Minimum}: \quad (1, -4)[/tex]

[tex]\textsf{Maximum}: \quad (-1, 0)[/tex]

Step-by-step explanation:

[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}}\implies f'(x) > 0[/tex]

[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies f'(x) < 0[/tex]

Given function:

[tex]f(x)=x^3-3x-2[/tex]

Differentiate the given function:

[tex]\implies f'(x)=3x^2-3[/tex]

To find the interval where f(x) is increasing, set the differentiated function to more than zero:

[tex]\implies 3x^2-3 > 0[/tex]

[tex]\implies 3(x^2-1) > 0[/tex]

[tex]\implies x^2-1 > 0[/tex]

[tex]\implies x^2 > 1[/tex]

[tex]\implies x < -1, \;\;\; x > 1[/tex]

So the interval on which function f(x) is increasing is:

[tex](- \infty, -1) \cup (1, \infty)[/tex]

To find the interval where f(x) is decreasing, set the differentiated function to less than zero:

[tex]\implies 3x^2-3 < 0[/tex]

[tex]\implies 3(x^2-1) < 0[/tex]

[tex]\implies x^2-1 < 0[/tex]

[tex]\implies x^2 < 1[/tex]

[tex]\implies -1 < x < 1[/tex]

So the interval on which function f(x) is decreasing is:

[tex](-1, 1)[/tex]

To find the relative extrema, set the differentiated function to zero and solve for x:

[tex]\implies 3x^2-3=0[/tex]

[tex]\implies 3(x^2-1)=0[/tex]

[tex]\implies x^2-1=0[/tex]

[tex]\implies x^2=1[/tex]

[tex]\implies x=-1,\;\;x=1[/tex]

To find the y-coordinates of the relative extrema, substitute the found values of x into the function and solve for y:

[tex]\implies f(-1)=(-1)^3-3(-1)-2=0[/tex]

[tex]\implies f(1)=(1)^3-3(1)-2=-4[/tex]

Therefore the minimum and maximum points of the function are:

[tex]\textsf{Minimum}: \quad (1, -4)[/tex]

[tex]\textsf{Maximum}: \quad (-1, 0)[/tex]

The distance that the light travels in the scientific notation will be 2.79 × 10⁹ miles.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

The light travels at a speed of 1.86 × 10⁵ miles per second. And it takes about 15,000 seconds for the light to reach Neptune.

Then the number of miles is given as,

1.86 × 10⁵ = d / 15,000

d = 1.86 × 10⁵ × 15,000

d = 2.79 × 10⁹ miles

The distance that the light travels in the scientific notation will be 2.79 × 10⁹ miles.

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The value of the sum notation is 729

From the question, we have the following parameters that can be used in our computation:

The sum notation

From the notation, we have the following values

First term, a = 972

Common ratio, r = -1/3

The sum is then represented as

Sum = a/(1 -r)

So, we have

Sum = 972/(1 + 1/3)

Evaluate

Sum = 729

Hence. the sum is 729

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Answer:

alex exercised 2 hours

Answer: 2

Step-by-step explanation:

we know that samn excersided 6 TIME AS MANY as alex. and that he excersides 12 hrs (dudes buff)

so we must divide 6/12

6/12=2

have a good day

Answer:12.90

Step-by-step explanation:

The value of f(0) is -2.

Option A is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

From the graph, we see that,

f(x) = -1 for -1 ≤ x < 0

Similarly,

f(x) = -2 for 0 ≤ x < 1 _____(1)

Now,

The value of f(x) at x = 0.

From (1),

f(0) = -2

Thus,

The value of f(0) is -2.

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Answer: y = 5x - 3

Step-by-step explanation:

The lines need the same slope

2 = 5(1) + b

2 = 5 + b

-5   -5

-3 = b

y = 5x - 3

The probabilities are (a) 0.8 (b) 0.125 (c) 0.12 (d) 0.1667 (e) 0.88 (f) 0.2045 (g) 0.795

Let A = meet specification, B = reground and C = scrapped

index 1 indicates the value was not reground and index 2 indicates that value was reground before obtaining the situation.

P(A₁) = 70% = 0.7

P(B) = 20% = 0.2

P(C₁) = 10% = 0.1

P(A₂/B) = 90% = 0.9

P(C₂/B) = 10% = 0.1

(a) Probability that a valve is ground only once = 1 - P(B)

                                                                              = 1 - 0.2 = 0.8

(b) a valve is not reground, the probability that it is scrapped

P(A₁∪C₁)

P(A₁) + P(C₁) = 0.1 + 0.7 = 0.8

P(C₁/A₁∪C₁) = 0.1/0.8 = 0.125

(c) Probability that a valve is scrapped

P(C₁) + P(B) × P(C₂/B) = 0.1 + 0.2 × 0.1

                                = 0.12

(d) a valve is scrapped, the probability that it was ground twice

P(B/C) = P(B∩C)/P(C)

          = [tex]\frac{0.2\times 0.1}{0.12}[/tex]

P(B/C) = 0.1667

(e) the probability that the valve meets the specification (after either the first or second grind)

P(A) = P(A₁) + P(B) × P(A₂/B)

P(A) = 0.7 + 0.2 × 0.9 = 0.88

(f) P(B/A) = P(A₂)/P(A)

              = 0.18/0.88 = 0.2045

(g) valve meets the specification, probability that it was ground only once

1 - P(B/A) = 1 - 9/14

= 0.795

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With a mean of $32,500 and a standard deviation of $2,500. The z-score for a sales associate who earns $37,500 is 2.

The z-score, also known as a standard score, is a measure of how many standard deviations a given value is from the mean. It is used to standardize the data and make it easier to compare and interpret. The formula for the z-score is:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

In this case, the mean annual salary for sales associates from a particular store is $32,500 and the standard deviation is $2,500. We want to find the z-score for a sales associate who earns $37,500. Plugging in the values, we get:

z = ($37,500 - $32,500) / $2,500 = 2

This means that the sales associate's salary is 2 standard deviations above the mean.

Interpreting the z-score can help us understand how unusual or typical a given value is in comparison to the mean. In this case, a z-score of 2 indicates that the sales associate's salary is relatively high compared to the mean, but it is not an extremely high salary.

We can use a standard normal table to find the proportion of the data that falls below a given z-score, or to find the corresponding value for a given proportion of the data.

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92 and 146 as product of their prime factor ​are 2^2 * 23 and 2 * 73

From the question, we have the following parameters that can be used in our computation:

92 and 146

Prime factorization of 92:

92 = 2 x 2 x 23

Prime factorization of 146:

146 = 2 x 73

So, we have

Product = 2 * 2 * 23 * 2 * 73

This gives

Product = 2^3 * 23 * 73

Hence, the expression is 2^3 * 23 * 73

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The probability that a newly arrived email which does mention "free gift card", is not spam is 0.0165.

Let S be the event that an email is spam, and let F be the event that an email mentions "free gift card". We want to find P(S' | F), the probability that the email is not spam given that it mentions "free gift card".

We can use Bayes' theorem to find P(S' | F):

P(S' | F) = P(F | S') P(S') / P(F)

We can calculate each of these probabilities as follows:

P(F | S') = the probability that a non-spam email mentions "free gift card". From the problem, we know that this probability is 0.005 (i.e., 99.5% of non-spam emails do not mention "free gift card").

P(S') = the probability that an email is not spam. From the problem, we know that this probability is 0.4 (i.e., 60% of emails are spam, so 40% are not spam).

P(F) = the probability that an email mentions "free gift card". This can be calculated using the law of total probability:

P(F) = P(F | S) P(S) + P(F | S') P(S')

= 0.20 × 0.60 + 0.005 × 0.40

= 0.121

In the first term, we use the given probability that 20% of spam emails mention "free gift card". In the second term, we use the probability that 0.5% of non-spam emails mention "free gift card".

Plugging these values into Bayes' theorem, we get:

P(S' | F) = 0.005 × 0.4 / 0.121 ≈ 0.0165

Therefore, the probability that a newly arrived email which does mention "free gift card" is not spam is approximately 0.0165 or 1.65%.

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Answer:

Step-by-step explanation:

197.97

The formula for the area of a circle is A = πr^2, where r is the radius.

The area of the circle with a radius of 3.5 centimeters is approximately 38.5 square centimeters.

Substituting r = 3.5 centimeters and using π ≈ 3.14, we get:

A = 3.14 × (3.5)^2

A = 38.465 square centimeters (rounded to the nearest tenth)

Consequently, the radius of the circle is 3.5 centimetres, and its area is roughly 38.5 square centimeters.

The area of a circle is the measure of the region enclosed by the circle in a two-dimensional space. It is the amount of space inside the circle and is typically measured in square units, such as square centimeters (cm²) or square meters (m²). The formula to calculate the area of a circle is:

Area = π x radius²

Where π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, which is approximately 3.14159, and radius is the distance from the center of the circle to any point on the circumference. The area formula can also be expressed in terms of the diameter:

Area = π x (diameter/2)²

This formula tells us that the area of a circle depends on the length of its radius or diameter, and it allows us to calculate the area of any circle given either of these two measurements.

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Answer: so u do 1 + n = 21

Step-by-step explanation:

21

Answer:

Step-by-step explanation:

SRS

The correct statement is option (B)  You are 90% confident that between 64.6% and 69.4% of all Americans would rank rear seat kickers as the most annoying on-board behavior of fellow passengers

The confidence interval created in the study was found to be between (0.646, 0.694), with a 90% level of confidence.

To interpret this interval, we can look at the options provided. Option A states that there is a 90% chance that the population proportion falls between 64.6% and 69.4%. This is not a correct interpretation, as it suggests that the proportion changes depending on the survey and is not fixed.

Option B, on the other hand, correctly states that we can be 90% confident that the true population proportion falls within the given range. This means that if we were to conduct the same survey many times, with different samples of 1000 Americans, we can expect the true population proportion to fall within this range in 90% of the surveys conducted.

Option C is incorrect, as it suggests that there is a 67% chance that the proportion falls within the given range, which is not the level of confidence used in the study.

Option D is also incorrect, as it only refers to the sample of 1000 passengers surveyed and not the entire population of Americans.

In summary, the confidence interval created in the Airplane Etiquette Study provides a range within which we can be 90% confident that the population proportion of Americans who rank rear seat kickers as the most annoying on-board behavior of fellow passengers falls. This interval does not change with repeated surveys and represents a fixed parameter of the population.

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Type I error is generally worse than a Type II error in all of these scenarios, as it can have more severe consequences.

The Null Hypothesis is a statement that assumes that there is no significant difference or effect between two groups or variables. The Alternative Hypothesis is a statement that assumes that there is a significant difference or effect between two groups or variables.

Conjecture: It is believed that a new drug can cure a cold.

Null Hypothesis: The new drug does not cure a cold.

Alternative Hypothesis: The new drug does cure a cold.

Type I error: We conclude that the drug cures a cold, but it does not.

Type II error: We conclude that the drug does not cure a cold, but it actually does.

Ramifications: If we make a Type I error, we may give the drug to people who do not need it, which can have negative side effects. If we make a Type II error, people who could have benefited from the drug will not receive it.

Conjecture: The teacher will never check homework today.

Null Hypothesis: The teacher will check homework today.

Alternative Hypothesis: The teacher will not check homework today.

Type I error: We conclude that the teacher will not check homework today, but they actually do.

Type II error: We conclude that the teacher will check homework today, but they actually do not.

Ramifications: If we make a Type I error, we may not do our homework and receive a lower grade. If we make a Type II error, we may waste time doing homework that will not be checked.

Conjecture: In a big store like Wal-Mart, they will never catch me if I shoplift.

Null Hypothesis: Wal-Mart will catch me if I shoplift.

Alternative Hypothesis: Wal-Mart will not catch me if I shoplift.

Type I error: We conclude that Wal-Mart will not catch us if we shoplift, but they actually do.

Type II error: We conclude that Wal-Mart will catch us if we shoplift, but they actually do not.

Ramifications: If we make a Type I error, we may shoplift and get caught, which can have legal consequences. If we make a Type II error, we may shoplift and get away with it, which can encourage further illegal behavior.

Conjecture: If I try to learn to ski, I will end up hurting myself.

Null Hypothesis: Trying to learn to ski does not result in injury.

Alternative Hypothesis: Trying to learn to ski does result in injury.

Type I error: We conclude that trying to learn to ski results in injury, but it actually does not.

Type II error: We conclude that trying to learn to ski does not result in injury, but it actually does.

Ramifications: If we make a Type I error, we may avoid skiing altogether and miss out on the experience. If we make a Type II error, we may attempt skiing and get injured, which can have physical and financial consequences

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Answer:

The z-score is a statistical measure that describes how far a sample estimate is from the population parameter in standard deviation units. It is calculated by taking the difference between the sample estimate and the population parameter, and dividing it by the standard deviation of the sampling distribution of the estimate. The resulting z-score can be used to calculate the probability of observing a sample estimate as extreme or more extreme than the one obtained, assuming the null hypothesis is true.

In this case, the sample estimate is the proportion of individuals who watch television primarily through streaming services, which is 70%, and the population parameter is the proportion of all individuals who watch television primarily through streaming services, which is 56%. The sample size is 350. The null hypothesis is that there is no difference between the sample and population proportions, and the alternative hypothesis is that the sample proportion is greater than the population proportion.

To calculate the z-score, we need to determine the standard error of the sampling distribution of the proportion. The standard error is a measure of the variability of sample estimates due to random sampling variation. It is calculated by taking the square root of the population proportion times one minus the population proportion, divided by the sample size. In this case, the standard error is:

standard error = sqrt[(0.56 * (1 - 0.56)) / 350] = 0.028

The z-score can now be calculated as:

z-score = (0.7 - 0.56) / 0.028 = 5.19

This z-score is quite large, indicating that the sample estimate is more than 5 standard errors away from the population parameter. This suggests strong evidence against the null hypothesis, as the probability of observing a sample estimate as extreme or more extreme than the one obtained is very low, assuming the null hypothesis is true.

In other words, the result of observing a sample proportion of 70% or above is highly unlikely to have occurred by chance alone, assuming that the true population proportion is 56%. This result provides evidence in support of the alternative hypothesis, which states that the sample proportion is greater than the population proportion.

The sample standard deviation of murder rates is approximately 2.2, and the sample variance is approximately 4.9. The standard deviation and variance are measured in the same units as the original data (murders per 100,000 inhabitants), squared and unsquared.

We can use a TI-83, TI-83 Plus, or TI-84 to calculate the sample standard deviation and variance of the murder rates:

We get the following results using this method:

2.209 is the sample standard deviation (s).

4.877 sample variance (s2) (rounded to three decimal places)

As a result, the sample standard deviation of the murder rates is about 2.2, and the sample variance is about 4.9. It should be noted that the standard deviation and variance are measured in the same units as the original data (murders per 100,000 inhabitants), squared and unsquared.

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