__Topic 1:__* The following data are monthly rents (in dollars) of studio and one-bedroom apartments in Harrisburg, Pennsylvania, in 2007, obtained from a random sample of such apartments advertised at rent.com in July 2007: {500, 549, 569, 575, 585, 600, 630, 680, 705, 790}. The mean of these ten rent prices is $618.30, and the standard deviation is $85.30.*

- Determine the
of the sample mean.__standard error__

- Describe what the population mean µ means in this context.

- Determine a 95% confidence interval for µ.

- Write a sentence interpreting what this interval means.

- Would you expect about 95% of the studio and one-bedroom apartments in Harrisburg in July 2007 to have a rent price within this interval? Explain.

__Topic 2:__* Students enrolled in an introductory statistics course at a university were asked to take a survey that indicated whether the student’s learning style was more visual or verbal. Each student received a numerical score ranging from -11 to +11. Negative scores indicated a visual learner, and positive scores indicated a verbal learner. The closer the score was to -11 or +11, the stronger the student’s inclination toward that learning style. A score of 0 would indicate neutrality between visual or verbal learning. For the 39 students who took the survey, the mean score was -2.744, and the standard deviation was 4.988.*

- State the null and alternative hypotheses for testing whether the mean score (among all students at this university) differs from 0.

- Calculate the value of the t-test statistic for the hypotheses stated in question 6

- Determine the p-value of the test as accurately as possible.

- Summarize the conclusion that you would draw from this test.

- Comment on whether the technical conditions of this t-test are satisfied.

__Topic 3:__*In a national study of American high school students in 2006, researchers asked students whether they have cheated on a test in the past year.*

1 and 2.) State the appropriate null and alternative hypotheses for testing whether the proportion of male students who admit to cheating is higher than that of female students.

*Researchers found that 61.8% of the male students admitted to cheating, compared to 58.3% of female students. *

3.) What further information would you need in order to conduct the test?

4.) What additional information would you ask about how the data were collected in order to check whether the technical conditions are met?

5.) Suppose the technical conditions are met and the test statistic turns out to be z = 6.32. Summarize the conclusion that you would draw from this test.

__Topic 4:__*Random samples of monthly rent prices, in dollars, for studio and one-bedroom apartments, were obtained for the Pennsylvania cities of Harrisburg and Philadelphia in July 2007. Summary statistics are calculated and shown below. Conduct a test of whether the sample data provide sufficient evidence at the = .10 significance level to conclude that the population mean** rent price differs between these two cities.*

6.) Null and alternative hypotheses

7.) Test statistic:

8.) p-value

9.) Test decision and conclusion in context.

10.) Check of technical conditions, mentioning any additional information that you would need to conduct this check

1.The National Institutes of Health funded a study of a random sample of 856 people age 71 and older in the United States. They found that 9.7% of these people suffer from Alzheimer’s disease.

** **

- Identify the population of interest in this study.
- Is .097 (the decimal version of 9.7%) a parameter or a statistic? What symbol do you use to represent it?
- Determine a 95% confidence interval for the proportion of elderly Americans who have Alzheimer’s disease.
- Check and comment on whether the technical conditions required for this confidence interval are satisfied.
- If you were to determine instead a 90% CI, how would it differ and how would it be similar to the result in part c? (Do not bother to do the calculations.)
- Determine how many people would have to be studied in a new sample if you want to estimate the population proportion to within ± .02 with 99% confidence. (Use the result of the current sample in your determination of the new sample size.)

2**.**Students in an introductory statistics class were asked how many states they have visited. The following output pertains to the sample results:

- Determine a 90% confidence interval for the population mean number of states visited among all students at this university.
- Check and comment on whether the technical conditions of this confidence interval are satisfied.
- For what proportion of students in the sample is the number of states visited within the interval calculated in part a?
- Should you expect your answer to part c to be close to 90%? Explain why or why not.
- Based on your interval, what can you say about the p-value if you were to conduct a two-sided significance test of whether the population mean differs from 15? Explain briefly, without conducting a test or doing new calculations.

3.It has been conjectured that two-thirds of all students have an active, as opposed to reflective, learning style. Data are available from a large sample of introductory statistics students at a public university in the eastern United States, who took a survey that assessed their learning style as active or reflective. Of the 962 students who participated, 596 were diagnosed as active learners and 366 as reflective learners.Use these sample data to conduct a significance test of the conjecture that two-thirds of all students have an active learning style. Report the hypotheses, test statistic, and p-value. Include a check of technical conditions. Also, indicate your test decision at the α = .05 significance level, and summarize your conclusion in context.

4.a. suppose you conduct a significance test and decide to reject the null hypothesis (H◦) at the α= .05 level. If you conduct the same test on the same data but instead use the α = .01 level, what decision would you make? (Circle your answer. Do not bother to explain.)

Reject (H◦) Fail to reject (H◦) Cannot say without more information

b. Suppose you conduct a significance test and decide to fail to reject the null hypothesis H0 at the α = .05 level. If you conduct the same test on the same data but instead use the α = .01 level, what decision would you make? (Circle your answer. Do not bother to explain.)

Reject (H◦) Fail to reject (H◦) Cannot say without more information

c. Suppose that we tell you that we flipped a coin multiple times and it landed heads 75% of the time. Would you be reasonably convinced that this was not a fair coin (where “fair” means that the coin has a .5 probability of landing “heads”)? If so, explain why. If not, describe what additional information you would ask for and explain why it is necessary.

5.Explain (briefly) what is wrong with each of the following sets of hypotheses:

- H0 : ? = 1.2 Ha : ?>1.2
- H0 : ?̂ = .5 Ha : pˆ > .5
- H0 : ? = 69 Ha : ? ≥ 69
- H0 : ? ≠ .5 Ha : ? = .5

6.Suppose you analyze data to assess whether the proportion of heart transplant deaths at St. George’s Hospital in London significantly exceeded the national benchmark rate of 15%.

a.Write a sentence describing what committing a Type I error would mean in this study.

b.Write a sentence describing what committing a Type II error would mean in this study.

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