Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire is interested in estimating the mean math SAT scores of the incoming class with 95% confidence. How large a sample should she take to ensure that the margin of error is below 29?

Answers

Answer 1

Using the z-distribution, it is found that she should take a sample of 46 students.

What is a z-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence, by the Empirical Rule the standard deviation is found as follows:

[tex]6\sigma = 800 - 200[/tex]

[tex]6\sigma = 600[/tex]

[tex]\sigma = 100[/tex]

The sample size is n when M = 29, hence:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]29 = 1.96\frac{100}{\sqrt{n}}[/tex]

[tex]29\sqrt{n} = 196[/tex]

[tex]\sqrt{n} = \frac{196}{29}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{196}{29}\right)^2[/tex]

n = 45.67.

Rounding up, a sample of 46 students should be taken.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1


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Answer:

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Answer:

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Answers

Answer:

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Answers

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Step-by-step explanation:

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Answers

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Answers

The answer is 6. When x is -3 then you divide -3 by 3 and the quotient is -1. So 5-(-1) is also equal to 5+1 which equals 6

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Answers

Answer:

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Answer:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Answers

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

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Answers

Answer:

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Required:
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b. What is the sample proportion indicating that their financial security was more that fair in 2012?In 2010?
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d. What is the 95% confidence interval estimate of the difference between the two population proportion?

Answers

Answer:

The calculated z = 2.85 falls in the critical region z > 1.96 so we accept the null hypothesis that there is no difference between the population proportions for the two years.

Step-by-step explanation:

Let p1 be the sample of 1000 adults chosen in 2012 and

p2 be the sample of 1100 adults chosen in 2010

Part a:

The hypothesis that can be used to test for a significant difference between the population proportions for the two years is:

H0: p1-p2= 0           against the claim      Ha: p1-p2≠0

Part b:

The sample proportion indicating that their financial security was more that fair in 2012 is

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p2^= 385/1100= 0.35

Part c:

p^c= 410+385/1000+1100= 0.3785

q^c= 1-p^c= 1-0.3785= 0.6124

The critical region is z > ±1.96

The test statistic is

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z= 0.41-0.35 /sqrt( 0.3785*0.6124(1/1000 +1/1100)

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z= 2.85

Conclusion

The calculated z = 2.85 falls in the critical region z > 1.96 so we accept the null hypothesis that there is no difference between the population proportions for the two years.

P- value :  0.00466

The result is significant( accept the null hypothesis) for  value less than 0.05

Part d:

                                                     2012                         2010

Sample                                       1000                           1100

Proportions                               0.41                             0.35

Standard Error               √0.41( 0.59)/1000        √0.35( 0.65)/1100

                                               = 0.0155                0.01438

Standard Error for the difference = √0.0155² + 0.01438² =0.0211

p1-p2 ± z* standard error for the difference

0.41-0.35 ± 1.96 *( 0.0211)

0.06 ± 0.041356

-0.018644,   0.101356

The 95 % confidence interval estimate is (-0.018644,   0.10135

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A line passes through the point (4, -3) and has a slope of
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Answers

Answer:

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Step-by-step explanation:

y = 4x + b

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Answers

Step-by-step explanation:

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Answers

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