# Point and Interval Estimates, Confidence Intervals, Levels of Significance and Hypothesis Testing

1. In your own words explain the difference between a point estimate and an interval estimate of a parameter? Which is better? Why?

2. What information is necessary to calculate a confidence interval? Is the size of the population relevant when one is determining the sample size for a confidence interval? What is necessary to determine the sample size?

3. Choose a variable and collect data consisting of at least 30 values. Before collecting the data, decide what a likely average might be, then complete the following:

a. Write a brief statement of purpose of the study

b. Define the population

c. State the hypotheses for the study

d. Select an  value

e. State how the sample was selected

f. Show the raw data

g. Compute the test statistic

h. Find the critical values(s)

i. State the decision

j. Summarize the results.

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

4. A sample of 40 golfers showed that their average on a particular course was 94 with a standard deviation of 6.

a. Find the 95% confidence interval of the mean score for all golfers.

b. Find the 95% confidence interval of the mean score for all golfers if a sample of 70 golfers is used instead of a sample of 40.

c. Which interval is smaller? Explain why.

5. A researcher is interested in estimating the noise levels in decibels at area urban hospitals. He wants to be 90% confident that his estimate is correct. If the standard deviation is 4.8, how large a sample is needed to get the desired information and to be accurate within 0.65 decibels?

6. A researcher claims that the average age of people who buy lottery tickets is 69. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation is 16. At  = 0.05 is there enough evidence to reject the researcher's claim?

49 63 90 52 22 80 72 56 82 56

24 46 70 74 70 61 65 71 39 74

79 76 71 49 62 68 71 67 69 45

7. A sample size of 45 is used to test H0:   75 vs. Ha:  < 75.

Given that = 72.9 and  = 4.3, answer the following questions

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?

8. List the steps involved in hypothesis testing using: a) the traditional/classical method; b) the probability-value method. Provide an example of each.

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