Answer:
[tex](a)[/tex] [tex]\bar x_1 = 9.94[/tex]
[tex](b)[/tex] [tex]x_2 = 10.4[/tex]
[tex](c)[/tex] [tex]\sigma_1 = 0.395[/tex]
[tex](d)[/tex] [tex]\sigma_2 = 0.231[/tex]
(e) There is sufficient evidence to reject the claim that the mean etch rate is the same for both solutions
[tex](f)[/tex] [tex]-0.75644 < \mu_1 - \mu_2 < -0.1556[/tex]
Explanation:
Given
Solutions 1 and 2
Solving (a): Mean of solution 1
For Solution 1, we have the following data:
[tex]9.8\ 10.4\ 9.4\ 10.3\ 9.3\ 10.0\ 9.6\ 10.3\ 10.2\ 10.1[/tex]
The sample mean is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
Where
[tex]n_1 = 10[/tex]
So, we have:
[tex]\bar x_1 = \frac{9.8+ 10.4+ 9.4+ 10.3+ 9.3+ 10.0+ 9.6+ 10.3+ 10.2+ 10.1}{10}[/tex]
[tex]\bar x_1 = \frac{99.4}{10}[/tex]
[tex]\bar x_1 = 9.94[/tex]
Solving (b): Mean of Solution 2
For Solution 1, we have the following data:
[tex]10.2\ 10.0\ 10.6\ 10.2\ 10.7\ 10.7\ 10.4\ 10.4\ 10.5\ 10.3[/tex]
The sample mean is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
Where
[tex]n_2 = 10[/tex]
So, we have:
[tex]x_2 = \frac{10.2+ 10.0+ 10.6+ 10.2+ 10.7+ 10.7+ 10.4+ 10.4+ 10.5+ 10.3}{10}[/tex]
[tex]x_2 = \frac{104}{10}[/tex]
[tex]x_2 = 10.4[/tex]
Solving (c): Sample Standard Deviation of solution 1
This is calculated as:
[tex]\sigma_1 = \sqrt{\frac{\sum (x-\bar x_1)^2}{n_1-1}}[/tex]
This gives:
[tex]\sigma_1 = \sqrt{\frac{(9.8 - 9.94)^2+ (10.4- 9.94)^2+ (9.4- 9.94)^2+................+ (10.2- 9.94)^2+ (10.1- 9.94)^2}{10 - 1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{1.404}{9}}[/tex]
[tex]\sigma_1 = \sqrt{0.156}[/tex]
[tex]\sigma_1 = 0.39496835316[/tex]
[tex]\sigma_1 = 0.395[/tex] --- approximated
Solving (d): Sample Standard Deviation of solution 2
This is calculated as:
[tex]\sigma_2 = \sqrt{\frac{\sum (x-\bar x_2)^2}{n_2-1}}[/tex]
So, we have:
[tex]\sigma_2 = \sqrt{\frac{(10.2 - 10.4)^2+ (10.0 - 10.4)^2+ (10.6 - 10.4)^2+ (10.2 - 10.4)^2+.......................+ (10.3 - 10.4)^2}{10-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{0.48}{9}}[/tex]
[tex]\sigma_2 = \sqrt{0.05333333333}[/tex]
[tex]\sigma_2 = 0.23094010766[/tex]
[tex]\sigma_2 = 0.231[/tex]
Solving (e): Test the hypothesis
[tex]H_0: \bar x_1 = \bar x_2[/tex]
[tex]H_1: \bar x_1 \ne \bar x_2[/tex]
Start by calculating pooled standard deviation
[tex]s_p = \sqrt{\frac{(n_1 - 1)*\sigma_1^2 + (n_2 - 1)*\sigma_2^2}{n_1 + n_2 -2}[/tex]
[tex]s_p = \sqrt{\frac{(10 - 1)*0.395^2 + (10 - 1)*0.231^2}{10+ 10-2}[/tex]
[tex]s_p = \sqrt{\frac{1.884474}{18}[/tex]
[tex]s_p = \sqrt{0.104693}[/tex]
[tex]s_p = 0.324[/tex]
Calculate test statistic
[tex]t = \frac{\bar x_1 - \bar x_2}{s_p\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}[/tex]
[tex]t = \frac{9.94 - 10.4}{0.324 * \sqrt{\frac{1}{10} + \frac{1}{10}}}[/tex]
[tex]t = \frac{-0.46}{0.324 * \sqrt{0.2}}[/tex]
[tex]t = \frac{-0.46}{0.324 * 0.4472}[/tex]
[tex]t = \frac{-0.46}{0.1448928}[/tex]
[tex]t = -3.175[/tex]
Calculate the degree of freedom
[tex]df = n_1 + n_2 - 2[/tex]
[tex]df = 10+10 - 2[/tex]
[tex]df = 18[/tex]
The p value is the in the column title of the student t distribution in row 18
[tex]p = 002621[/tex]
The p value is less than the significance level (0.05).
i.e.
[tex]p < 0.05[/tex]
So: Reject the null hypothesis
Solving (f): 95% two-sided confidence interval
[tex]c = 95\%[/tex]
Calculate the degree of freedom
[tex]df = n_1 + n_2 - 2[/tex]
[tex]df = 10+10 - 2[/tex]
[tex]df = 18[/tex]
Calculate [tex]\alpha[/tex]
[tex]\alpha = (1 - c)/2[/tex]
[tex]\alpha = (1 - 95\%)/2[/tex]
[tex]\alpha = (0.05)/2[/tex]
[tex]\alpha = 0.025[/tex]
Using student t distribution
[tex]t_{\alpha/2} = 2.101[/tex]
Calculate margin of error (E)
[tex]E = t_{\alpha/2} * s_p * \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}[/tex]
[tex]E = 2.101 * 0.324 * \sqrt{\frac{1}{10} + \frac{1}{10}}[/tex]
[tex]E = 2.101 * 0.324 * \sqrt{0.2}[/tex]
[tex]E = 0.3044[/tex]
The boundaries of the confidence are:
[tex](\bar x_1 - \bar x_2) -E[/tex] [tex]= (9.94- 10.4) - 0.3044 = -0.7644[/tex]
[tex](\bar x_1 - \bar x_2) + E[/tex] [tex]= (9.94- 10.4) + 0.3044 = -0.1556[/tex]
The confidence interval is:
[tex]-0.75644 < \mu_1 - \mu_2 < -0.1556[/tex]
imagine that you can time travel and you are going back to Ancient Persia.
In the same way that we picture what they might have looked like thousands of years ago describe to the Persians what a statue of a typical teenager living today would look like. Be descriptive and think about qualities that are trendy today.
Answer:
hi
Explanation:
IT would look like a aesthic girl and boy holding hands with bucket hats on and brown clothes
How much power should the
government have? Restrict your answer to what you have
learned in this lesson.
Answer:
A government should have enough power to protect and serve its citizens but not enough power to abuse it.
Explanation:
Why was Julius Caesar popular among the plebeians
Answer:
War heroGenerous to the commonersBeloved by soldiersExplanation:
Julius Caesar appealed to the plebeians who were the lower classes of Rome or the commoners, by being generous to them. He gave food and land to the poor and essentially redistributed some wealth from the wealthy of Rome to the commoners.
To top that off the Plebeians loved that Julius Caesar was a war hero who had conquered Gaul and also had fought alongside his soldiers in battle. This painted him as an efficient leader who did not hide behind privilege and they respected this.
PLZ EXPLAIN PLEASE
Based on the information in the chart, what can be concluded about Mexico?
A.
It was heavily influenced by Spain.
B.
It was heavily influenced by Portugal.
C.
It has remained free from European influence.
D.
Both A and B are correct.
Answer:
D
Explanation:
pretty sure its d
How can social stratification affect educational attainment?
Answer:
Directly, individuals from higher social classes are more likely to have the means to attend more prestigious schools, and are therefore more likely to receive higher educations. ... Just as education and social class are closely intertwined, stratification in education contributes to stratification in social class.
how will one adapt from ones post school social routine to minimize the impact that social pressures may have on your academic or work performance,?
Answer:
need points sorry
tell other
Explanation:
ahjajajajajajjajajajajs
Enumerate some of the values your family holds dear. In what ways do these values affect your lifestyle as a teenager?
In 10 sentences
How many times has the Pacific Conference won the NCAA Basketball championship?
The executive branch in Georgia is responsible for
interpreting laws.
enacting laws.
carrying out laws.
overriding laws.
Answer:
Option C- Carrying out laws.
Explanation:
What do Cuba and Brazil have in common?
Your answer:
The majority of tourists in both nations are from the United States.
The dominant language in both countries is Spanish.
Because of location, both countries have a tropical climate.
Answer:
c. because of location, both countries have a tropical climate
Explanation:
i'm not too sure about the tourist thing, but the dominant language in brazil is portuguese and the dominant language in cuba is spanish.
good luck :)
i hope this helps
have a nice day !!
Which of the following statements is true of masturbation? a. It is not useful when illness, absence, divorce, or death deprives a person of a partner. b. It produces the same physical responses as sexual activity with a partner. c. It involves sexual stimulation of a man's genitals by means of oral manipulation. d. It is the main cause of warts, blemishes, and blindness in men.
Answer: c. It involves sexual stimulation of a man's genitals by means of oral manipulation
Explanation:
Masturbation simply refers to thw stimulation of the genitals in order to derive sexual pleasure by an individual. This may either lead to orgasm or not.
It should be noted that masturbation doesn't cause warts, blemishes, and blindness in men. Also, it doesn't have same physical responses like having sex with one's partner.
Passing of genetic information from one generation to the next is called
Answer:
Heredity is defined as the passage of genetic instructions from one generation to the next.
Explanation:
How did the boll weevil impact the cotton industry in texas
Answer: The boll weevil created mass destruction in cotton crops as it fed on and set its eggs in the fruiting structures of the cotton plant.
What new technology was used in world war 1
A. Gas
B. Tanks
C. Machine guns
D. U-boats
E. All of the above
Answer:
C. Machine guns
Explanation:
Military technology of the time included important innovations in machine guns....
grenades, and artillery, along with essentially new weapons such as submarines, poison gas, warplanes and tanks.
_____________________ can declare war on another country. *
10 points
1.State governments
2.The Federal government
3.American citizens
4.A governor
Researchers for Hershey Chocolate observe shoppers who buy chocolates and other candies. After shoppers make their purchase, the researchers, standing at the end of the aisle, ask a few demographic and psychographic questions to better know who the buyers are. Then they give the shoppers some free chocolates for their time. What kind of research is this
Answer:
Ethnographic research
Explanation:
Ethnographic research is a research method that studies behaviour of people in their own environment. This method uses methods such as face to face observation and interviewing. The objective of this is to provide a detailed description of the needs of the customers so that the product can be designed accordingly.
Thus, when Hershey Chocolate observe shoppers who buy chocolates and other candies. After shoppers make their purchase, the researchers, standing at the end of the aisle, ask a few demographic and psychographic questions to better know who the buyers are. Then they give the shoppers some free chocolates for their time. This is an example of ethnographic research.
Which of the following is one reason that unions play a decreased role in the US economy today?
A.
Many large US factories have closed as companies seek lower-priced labor elsewhere.
B.
Over time, the collective bargaining process has helped define acceptable actions for management and labor.
C.
Long-time union efforts have led to higher wages and improved working conditions.
D.
Regulations established by the US government have limited the effectiveness of unions.
Answer:
A
Explanation:
Items whose price was HIGH because the supply was
Answer:
Low, so in high demand
Explanation:
At what age did ophra winfrey start her innovation
Answer:
17
Explanation:
World War II began as a fight against against which of the following?
Communism
Communism
Nationalism
Nationalism
Capitalism
Capitalism
Fascism
Answer:
Fascism
Explanation:
World War 2 began when Britain and France declared war on Nazi Germany two days after they invaded Poland.
Answer:
nationalism
Explanation:
Among the reasons socialism never developed in the United States was that labor
unions:
A) Secured workers' rights
B) Broke up monopolies
C) Guaranteed health care
D) Diversified the workforce
Answer:
A)
Explanation:
The territory acquired in the Mexican-American War is called the
Answer:
It ended the war, and Mexico recognized the Mexican Cession, areas not part of disputed Texas but conquered by the U.S. Army. These were northern territories of Alta California and Santa Fe de Nuevo México. ... The question of how to treat the new acquisitions also intensified the debate over slavery in the United States
Explanation:
i hope you understand better
Answer:
its the second drop down
Explanation:
Over time the average rate of return on stocks is
about 10% per yearrrrrr
All of the following are true about presidential appointments to the Supreme Court EXCEPT Question 8 options: presidents usually appoint people who belong to the president’s political party. presidents see their appointments as a way to institutionalize their political views long after they have left office. Republican presidents have usually appointed liberal justices. President Bush appointed two justices to the Court. President Clinton appointed many judges to the district and appeals courts.
Answer:
Republican presidents have usually appointed liberal justices.
Explanation:
President Bush has appointed 327 federal judges, two of whom have been appointed to serve on the U.S. Supreme Court. President Clinton also appointed a large number of judges, 378 in total, where 66 of them were appointed to serve on the District and Appeal Courts. These nominations are usually made within the president's own party and serve to give him information about the government even after leaving office.
Accordingly, we can eliminate and consider the option "Republican presidents have usually appointed liberal justices" to be incorrect.
what is the important reason why students should learn and develop 21st century skills?
Answer:
21st-century skills are more important to students than ever before. They provide a framework for successful learning but also ensure students can thrive in a world where change is consistently occuring and learning never stops.
what is parallel culture
Which BEST explains why GDP per Capial is a more accurate measure of eacnomic strength than GDP alone?
O A. GDP take sinto account population while GDP per Capital does not use that in the equation.
B. GDP per Capital factors population into the formula to offset countries with high GDPs and high populations.
O C. GDP per capital is not an accurate measure of economic strength since it doesn't take into account the system of government.
D. GDP per Capital take sinto account economic systems into the equation while GDP does not.
which 5 strategies can You employ to ensure that you as a student you will not drop out of university
Answer:
*study
*get motivated
* find friends so you will be less likely to leave
*do something you want to do
*have fun
* go to a university you want to go to
Explanation:
What law always overrides any other when there is a conflict?
A. Federal Law
B. State Law
C. Local Law
PLZ HELP ILL COUNT YOU AS BRAINLIES!!
Answer:
The federal law always overrides when there is conflict
10 points Which of the following issues relates most to foreign policy?
A. Health care
B. Jobs
C. Taxes
D. Weapons
Answer:
D. Weapons
Explanation:
Healthcare, jobs, and taxes are issues that only deal with the people living in the country. But weapons are bought and sold by different countries around the world and are used in wars.