Chapter 23, 24, 25

A golf instructor is interested in how much improvement individual beginner golf class students make during the course of the 4 week clinic she teaches each summer. Before the clinic began, each golfer played all 18 holes of the course and the score for each round was recorded. The same was done when the players completed the clinic. Which is the correct hypothesis test for this situation?

A golf instructor is interested in how much improvement individual beginner golf class students make during the course of the 4 week clinic she teaches each summer. Before the clinic began, each golfer played all 18 holes of the course and the score for each round was recorded. The same was done when the players completed the clinic. Which is the correct hypothesis test for this situation? Answer: Matched Pairs Mean T Test

A cruise line is trying to determine if there is a difference in the mean amount of money passengers spend on board their ships during a 1 week cruise to Alaska and a 1 week cruise to Mexico. A random sample of 35 passengers is taken from the Alaskan cruise; a random sample of 30 passengers is taken from the Mexican cruise. Is there a significant difference between the mean amounts spent by passengers on the two cruise ships?

A cruise line is trying to determine if there is a difference in the mean amount of money passengers spend on board their ships during a 1 week cruise to Alaska and a 1 week cruise to Mexico. A random sample of 35 passengers is taken from the Alaskan cruise; a random sample of 30 passengers is taken from the Mexican cruise. Is there a significant difference between the mean amounts spent by passengers on the two cruise ships?

Answer: Two Sample Mean T-Test

At North High School the average number of cars owned by a family is 2.35. South High School is in a more affluent area of the town and students claim they have on average more cars per family. An SRS of 36 students from South High School was selected and they were asked how many cars in each of their families.

At North High School the average number of cars owned by a family is 2.35. South High School is in a more affluent area of the town and students claim they have on average more cars per family. An SRS of 36 students from South High School was selected and they were asked how many cars in each of their families. Answer: 1 Sample Mean T-Test

An occupational safety administrator is interested in reducing repetitive motion injuries for office workers who use computers. The administrator divides 48 volunteers at random into two groups. The first group will use a standard keyboard for 12 months. The second group will use a new keyboard design for the same period of time. At the end of the study the frequencies of volunteers experiencing repetitive motion injuries with their respective keyboards will be compared.

An occupational safety administrator is interested in reducing repetitive motion injuries for office workers who use computers. The administrator divides 48 volunteers at random into two groups. The first group will use a standard keyboard for 12 months. The second group will use a new keyboard design for the same period of time. At the end of the study the frequencies of volunteers experiencing repetitive motion injuries with their respective keyboards will be compared.

Answer: Two Sample Proportion Z-Test

A hypothesis test is conducted with respect to the mean weight (in ounces) of potato chip bags from a certain manufacturer. The test’s hypotheses are and . Which confidence interval below would support the conclusion that there is insufficient evidence to reject the null hypothesis at the level of significance?

A) The 97% confidence interval for the mean weight in ounces of potato chips is (0.765, 0.823).

B) The 94% confidence interval for the mean weight in ounces of potato chips is (0.765, 0.823).

C) The 97% confidence interval for the mean weight in ounces of potato chips is (0.725, 0.783).

D) The 94% confidence interval for the mean weight in ounces of potato chips is (0.725, 0.783).

E) We cannot conclude anything with a confidence interval unless we have the actual data set to construct the interval.

oH : .8 H : .8a

0.03

A hypothesis test is conducted with respect to the mean weight (in ounces) of potato chip bags from a certain manufacturer. The test’s hypotheses are and . Which confidence interval below would support the conclusion that there is insufficient evidence to reject the null hypothesis at the level of significance?

A) The 97% confidence interval for the mean weight in ounces of potato chips is (0.765, 0.823).

B) The 94% confidence interval for the mean weight in ounces of potato chips is (0.765, 0.823).

C) The 97% confidence interval for the mean weight in ounces of potato chips is (0.725, 0.783).

D) The 94% confidence interval for the mean weight in ounces of potato chips is (0.725, 0.783).

E) We cannot conclude anything with a confidence interval unless we have the actual data set to construct the interval.

oH : .8 H : .8a

0.03

A significance test was performed with hypotheses of and . The P-value for the test was 0.026. Which of the following conclusions is most appropriate for this test?

A) 2.6% of the time the mean will be exactly 15.

B) 97.4% of the time the mean will be less than 15.

C) There is a 2.6% chance of making a Type II error.

D) There is reason to believe that the mean, µ is less than 15.

E) The true mean is approximately 2.6% of 15.

oH : 15 H : 15a

A significance test was performed with hypotheses of and . The P-value for the test was 0.026. Which of the following conclusions is most appropriate for this test?

A) 2.6% of the time the mean will be exactly 15.

B) 97.4% of the time the mean will be less than 15.

C) There is a 2.6% chance of making a Type II error.

D) There is reason to believe that the mean, µ is less than 15.

E) The true mean is approximately 2.6% of 15.

oH : 15 H : 15a

A light bulb manufacturer wishes to estimate the mean lifetime (in hours) of its new “long-life” bulb. Thirty bulbs were tested and the lifetime was recorded for each. The mean of the sample was 1,450 hours and the standard deviation of the sample was 150 hours. Assuming all conditions for inference are satisfied, what is the 99% confidence interval for µ, the mean lifetime of the new “long-life” bulb?

150 150A) 1450 2.750 B) 1450 2.756

30 30150 150

C) 1450 2.750 D) 1450 2.75629 29

150E) 1450 .8389

29

A light bulb manufacturer wishes to estimate the mean lifetime (in hours) of its new “long-life” bulb. Thirty bulbs were tested and the lifetime was recorded for each. The mean of the sample was 1,450 hours and the standard deviation of the sample was 150 hours. Assuming all conditions for inference are satisfied, what is the 99% confidence interval for µ, the mean lifetime of the new “long-life” bulb?

150A) 1450 2.750

30150 150

C) 1450 2.750 D) 1450 2.756

150

29 29150

E)

B) 145

1450 .

0 2.7

8389

5630

29

A professor at a large university believes that students take an average of 15 credit hours per term. A random sample of 24 students in her class of 250 students reported the following number of credit hours that they were taking:

Does this sample indicate that students are taking more credit hours than the professor believes? Test an appropriate hypothesis and state your conclusion.

12 13 14 14 14 15 15 15 16 16 16 16

17 17 17 18 18 18 18 19 19 19 20 21

A professor at a large university believes that students take an average of 15 credit hours per term. A random sample of 24 students in her class of 250 students reported the following number of credit hours that they were taking:

Does this sample indicate that students are taking more credit hours than the professor believes? Test an appropriate hypothesis and state your conclusion. Answer: Reject the null since p-val = .001, which is less than alpha = .05. t = 3.307

12 13 14 14 14 15 15 15 16 16 16 16

17 17 17 18 18 18 18 19 19 19 20 21

Confidence Interval Basics

Suppose you have calculated a confidence interval for a population mean and got (15.66, 17.54) based on a sample of size 30. with a standard deviation of 2.22.

sample mean = ME = SE= t* = Confidence Level =

Confidence Interval Basics

Suppose you have calculated a confidence interval for a population mean and got (15.66, 17.54) based on a sample of size 30. with a standard deviation of 2.22.

sample mean = 16.6 ME = .94 SE= .4053 t* =2.319 Confidence Level =97.2%

Hypotheses & define Parameter Assumptions & formula

◦ Be sure to list the assumptions and check them, plot the graph and give a comment. Write the correct formula for the test statistic including t =

Mechanics◦ List the value of t, degrees of freedom, and the p-

value. Decision & Conclusion

◦ Write the decision to either Fail to reject or Reject and state why according to the p-value. Write the conclusion in context of the situation.

Assumptions◦ List and check the assumptions. If you are given

data, plot it and write a description that indicates the Nearly Normal Model condition is met.

Formula and interval Conclusion

◦ We are 95% confident that ….