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P-Values and Mean Differences

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31. A new weight-watching company, Weight Reducers International, advertises that those who join will lose, on the average, 10 pounds the first two weeks with a standard deviation of 2.8 pounds. A random sample of 50 people who joined the new weight reduction program revealed the mean loss to be 9 pounds. At the .05 level of significance, can we conclude that those joining Weight Reducers on average will lose less than 10 pounds? Determine the p-value.

32. Dole Pineapple, Inc., is concerned that the 16-ounce can of sliced pineapple is being overfilled. Assume the standard deviation of the process is .03 ounces. The quality control department took a random sample of 50 cans and found that the arithmetic mean weight was 16.05 ounces. At the 5 percent level of significance, can we conclude that the mean weight is greater than 16 ounces? Determine the p-value.

38. A recent article in The Wall Street Journal reported that the 30-year mortgage rate is now less than 6 percent. A sample of eight small banks in the Midwest revealed the following 30-year rates (in percent):
4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6

At the .01 significance level, can we conclude that the 30-year mortgage rate for small banks is less than 6 percent? Estimate the p-value.

27. A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. The information is summarized below.
Statistic Men Women
Sample mean 24.51 22.69
Population standard deviation 4.48 3.86
Sample size 35 40

At the .01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? What is the p-value?

46. Grand Strand Family Medical Center is specifically set up to treat minor medical emergencies for visitors to the Myrtle Beach area. There are two facilities, one in the Little River Area and the other in Murrells Inlet. The The Quality Assurance Department wishes to compare the mean waiting time for patients at the two locations. Samples of the waiting times, reported in minutes, follow:

Location Waiting Time
Little River 31.73 28.77 29.53 22.08 29.47 18.60 32.94 25.18 29.82 26.49
Murrells Inlet 22.93 23.92 26.92 27.20 26.44 25.62 30.61 29.44 23.09 23.10 26.69 22.31

Assume the population standard deviations are not the same. At the .05 significance level, is there a difference in the mean waiting time?

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This solution provides calculations and explanations for p-values and mean differences.

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Statistical Tests, Hypothesis Testing, p-Values, and Sample Size

1. Classify the following as independent or dependent samples:

a. The effectiveness of two blood pressure medicines on two groups of patients.
b. Measures of gas mileage and speed for a group of racecars.
c. Scores of a group of nurses on the NCLEX nursing license exam.

2. Please answer the following.

a. Explain the difference between testing a single mean and testing the difference between two means.

b. What two assumptions must be met when one is using z test to test differences between two means?

c. When can the sample standard deviations s1 and s2 be used in place of the population standard deviations 1 and 2?

3. Choose a variable. Before you simulate collecting the data, decide what a likely average might be and list all data in part e.; then complete the following:

a. Write a brief statement of purpose of the study and the population to be studied
b. State the hypotheses for the study
c. Select an  value
d. Display all the raw data
e. Decide which statistical test is appropriate and compute the test statistic (z or t). Find the critical values(s)

f. State the decision and summarize the results in a paragraph.

You may obtain raw data from the random number table in the appendix section of your text or from any other sources; including sources on the World Wide Web.

4. Please answer each question below.

a. In what ways is the t distribution similar to the standard normal distribution?

b. In what ways is the t distribution different from the standard normal distribution?
Please specify how the formula for the t test differs from the formula for the z test?

5. Complete the following:

a. Select a variable. Compare the mean of the variable for a sample of 30 for one group with the mean of the variable for a sample of 30 for a second group. Show a hypothetical set of data with a hypothetical mean and standard deviation and show all calculations for conducting a z test with these data.

b. Select a variable. Compare the mean of the variable for a sample of 10 for one group with the mean of the variable for a sample of 10 for a second group. Show a hypothetical set of data with a hypothetical mean and standard deviation and show all calculations for conducting a t test with these data.

c. Select a variable that will enable you to compare proportions of two groups. Use sample sizes of at least 30. Use the z test for proportions to analyze the data.

You may obtain raw data from the random number table in the appendix section of your text or from any other sources; including sources on the World Wide Web.

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