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Confidence Interval and Hypothesis Test

1. A sample of 35 golfers showed that their average score on a particular golf course was 80 with a standard deviation of 6.
Answer each of the following (show all work):
(A) Find the 95% confidence interval of the mean score for all 35 golfers.
(B) Find the 95% confidence interval of the mean score for all golfers if this is a sample of 50 golfers instead of a sample of 35.
(C) Which confidence interval is smaller and why?

2. Consider the sample data below.
46 50 54 50 54 34 36 53 45 47 46
50 46 51 33 53 52 40 50 45 46 45
46 44 43 42 51 45 36 39 45 54 45

Suppose we wish to test the following hypotheses for the data:
Calculate the mean and the standard deviation of the data as above:

(A) Compute the appropriate test statistic for testing (show all work).
(B) Determine the critical value for alpha = 0.05.
(C) Test using the traditional/classical method.
(D) State the decision based on the results of the test.
(E) Had you used the p-value method of hypothesis testing, what would the p-value have been?

3. A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 95% confident that her estimate is correct. If the standard deviation is 4.8, how large a sample is needed to get the desired information to be accurate within 0.70 decibels? Show all work.

4. (please refer to the attachment for the given data)

(A) What is the computed value of the test statistic?

(B) What distribution does the test statistic have when the null hypothesis is true?

(C) Is the alternative hypothesis one-tailed or two-tailed?

(D) What is the p-value?

5. A researcher claims that the average age of people who buy lottery tickets is 60. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation is 14. At alpha = 0.05 is there enough evidence to reject the researcher's claim? Show all work.

65 63 75 52 22 80 72 56 82 56
24 60 70 65 70 61 65 71 39 74
79 75 71 49 62 68 71 67 69 60

6. Given a level of confidence of 95% and a population standard deviation of 6, what other information is necessary:
(A) To find the Maximum Error of Estimate (E)?

(B) To find the sample size (n)?

(C) Given the above confidence level and population standard deviation, find the Maximum Error of Estimate (E) if n = 45. Show all your calculations. Show all work.

(D) For this same sample of n = 45, what is the width of the confidence interval around the population mean? Show all work.

(E) Given this same confidence level and standard deviation, find n if E = 2.00. (Always round to the nearest whole person.) Show all work.

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Solution Summary

The solution provides step-by-step calculations of confidence interval, maximum error of estimate, required sample size etc. The solution also provides step-by-step method of performing hypothesis test. All the steps of hypothesis testing (formulation of null and alternate hypotheses, selection of significance level, choosing the appropriate test-statistic, decision rule, calculation of test-statistic, p-value and conclusion) have been explained in details.

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