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# Compare the Concepts of Estimation and Hypothesis

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11. From the population of unknown mean &#956; and a standard deviation &#963; = 5.0, a sample of n= 100 is selected and the sample mean 40.6 is found. Compare the concepts of estimation and hypothesis testing by answering the following:

a. Determine the 95% confidence interval for &#956;.
b. Complete the hypothesis test involving Ha : &#956; &#61625; 40 using the p-value approach and
&#945; = 0.05.

12. From a population of unknown mean &#956; and a standard deviation &#963; = 5.0, a sample of n= 100 is selected and the sample mean 40.9 is found. Compare the concepts of estimation and hypothesis testing by answering the following:
a. Determine the 98% confidence interval for &#956;.
b. Complete the hypothesis test involving Ha : &#956; > 40 using the p-value approach and &#945; =0.05.

13. An article titled "Evaluation of a Self-Efficacy Scale for Preoperative Patients" describes a 32-item rating scale was administered to 200 preoperative patients. The mean efficiency expectation score for the ambulating item equaled 4.00. Construct the 0.95 confidence interval for the mean of all such preoperative patients. Use &#963; = 0.94.

14. According to the article in Health magazine, supplementation with potassium reduced the blood pressure readings in a group of mild hypertension patients from an average of 158/100 to 143/84.5. Consider a study involving the use of potassium supplementation to reduce the systolic blood pressure for mild hypertensive patients. Suppose 75 patients with mild hypertension were places in potassium for 6 weeks. The response measured was the systolic reading was 12.5 units. Assume the population standard deviation, , to be 7.5 units. Calculate the value if the test statistic z * and the p-value for testing
Ha : &#956; &#61501;&#61472;&#61489;&#61488;&#61486;&#61488;&#61472;vs. Ha : &#956; &#61502;&#61472;&#61489;&#61488;&#61486;&#61488;

15. Worker honey bees leave the hive on a regular basis and travel to flowers and other resources of pollen and nectar before returning to the hive to deliver their cargo. The process is repeated several times each day in order to feed younger bees and support the hive's production of honey and wax. The worker bee can carry an average of 0.0113 gm of pollen and nectar per trip, with a standard deviation of 0.0063 g. Fuzzy Drone is entering the honey and beeswax business with a new strain of Italian Bees that re reportedly capable of carrying larger loads of pollen and nectar than the typical honey bee. After installing three hives, Fuzzy isolated bees before and after their return trip
and carefully weighed their cargoes. The sample mean weight of the pollen and nectar was 0.0124 gm. Can Fuzzy's bees carry greater load of pollen and nectar than the rest of the honey bee population? Complete the appropriate hypothesis test at the 0.01 level of significance.
a. Solve using the p-value approach
b. Solve using the classical approach

16. One of the objectives of a large medical study was to estimate the mean physician fee for cataract removal for 25 randomly selected cases the mean fee was found to be \$1,550 with a standard deviation of \$125. Set a 99% confidence interval on &#956; , the mean fee for all physicians. Assume the fees are normally distributed.

17. The water pollution reading at State Park Beach see to be lower than last year. A sample of 12 readings was randomly selected from the records of this years daily readings:

3.5 3.9 2.8 3.1 3.1 3.4 4.8 3.2 2.5 3.5 4.4 3.1

Does this Sample provide sufficient evidence to concluded that the mean of this year's pollution readings is significantly lower than last year's mean of 3.8 at the 0.05 level? Assume that all such readings have a normal distribution.

18. A company is drafting an advertising campaign that will involve endorsements by noted athletes. In order for the campaign to succeed, the endorser must be both highly respected and easily recognized. A random sample of 100 prospective customers are shown photos of various athletes. If the customer recognizes an athlete, then the customer is asked whether he or she respects the athlete. In the case of the top woman golfer, 16 of the 100 respondents recognized her picture and indicated that they also respected her. At the 95% level of confidence, what is the true proportion with which this woman golfer is both recognized and respected?

19. Prevention Magazine reported in its latest survey that 64% of adult Americans, or 98 million people, were overweight. The telephone survey of 1254 randomly selected adults was conducted Nov. 8-29, 1990, and had a margin of error of three percentage points.
a. Calculate the maximum error of estimate for 0.95 confidence with p'=0.64
b. how large a sample would be needed to reduce the maximum error to 0.02 with 95% confidence?

20. A production process is considered out of control if the produced parts have a mean length different from 27.5 mm or a standard deviation that is greater than 0.5 mm. A sample of 30 parts yields a sample mean of 27.63 mm and a sample standard deviation of 0.87 mm. If we assume part length is a normally distributed variable, does this sample indicate that the process should be adjusted in order to correct the standard deviation of the product? Use &#945; = 0.05.
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