Date : Novemver 28, 2007 (Wednesday) Time: 9:15-10:20 Place: SCI. 3550 Examination Type: Closed notes and books. But you will be allowed to use one sheet of paper (information sheet) with the formulas and facts that you need (This sheet should not have solutions of problems or examples) The things that you need for the exam: Photocopies of Tables given to you earlier. Coverage: Chapter 6.3-9.4 (included)

The important topics that you should know for the exam.

Chp. 6 Sampling Distributions The difference between parameter and statistics 6.1 Sampling distribution Finding sampling distribution of a statistics Finding the mean and standard deviation of a sampling distribution 6.2 Properties of sampling distribution Point estimator Unbiased estimate Biased estimate Minimum variance estimator 6.3 Central Limit Theorem (CLT) Sampling distribution of sample mean The mean The standard deviation = standard error Approximate distribution of the sample mean for large n (CLT)

Chp. 7 Estimation with Confidence Intervals 7.1 Large Sample Confidence intervals for the m 7.2 Small Sample Confidence Intervals for the m 7.3 Confidence Interval for a Population Proportion, p. 7.4 Determination of Sample Size For the Population Mean For the Population Proportion

Chp. 8 Tests of Hypotheses 8.1 Elements of Tests of Hypothesis 8.2 Large Sample Test of Hypothesis About m 8.3 Observed Significance Level: P-Value 8.4 Small Sample Test of Hypothesis About m 8.5 Test of Hypothesis About the Population Proportion, p.

1. Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats. To accomplish this, the records of 225 flights are randomly selected, and sample mean is found to be 11.6 seats. Assume that the population standard deviation is known to be 4.1 seats. a. Estimate m= the mean number of unoccupied seats per flight during the past year, using a 90% confidence interval. b. How large a sample needs to be taken to estimate the mean number of unoccupied seats to within 0.35 seats with 90% confidence? c. Test the hypothesis H0: m=13 seats against the hypothesis Ha: m 13 at a=0.01 level. d. Find the p-value of the test.

2. A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 15% of the women who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 70 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in six. a. State the null and alternative hypotheses. b. Define Type I and Type II errors in the context of the problem. c. Do the data provide sufficient evidence to indicate that the new screening method is better than the one currently in use? Use a=0.05. d. Find the prob-value (p-value) of the test e. Using a 95% confidence interval, estimate the proportion of the women with breast cancer that the new method will fail to detect.

3. A state game protector collects measurements on the weights of species of fish in a lake. The standard deviation of the weights is known to be 2.13 pounds. A total of 49 measurements are obtained and it is determined that sample mean is 7.34. a. Give a 95% confidence interval for the average weight of that species. b. How many measurements must be averaged to get a margin of error of +- 0.5 (with a bound of error of 0.5) (the mean to be within 0.5) with 95% confidence?

4. The manufacturer of a certain foreign car sold in the United States claims that it will average 35 miles per gallon of gasoline with the standard deviation of 9.3 miles. To test this claim, a consumer's group randomly selects 40 of these cars and drives them under normal driving conditions. These cars average 28 miles to the gallon. Does this sample indicate that average mileage is more than 35? a. State the null and alternative hypotheses b. Carry out the test and give the P-value. Report your conclusion. c. Is the result significant at the 5% level?

5. Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats. To accomplish this, the records of 225 flights are randomly selected, and sample mean is found to be 11.6 seats. Assume that the population standard deviation is known to be 4.1 seats. a. Estimate m= the mean number of unoccupied seats per flight during the past year, using a 90% confidence interval. b. How large a sample needs to be taken to estimate the mean number of unoccupied seats to within 0.35 seats with 90% confidence? c. Test the hypothesis H0: m=13 seats against the hypothesis Ha: m 13 at a=0.01 level. d. Find the P-value of the test.

6. A fast food restaurant is considering a new product. It will be worthwhile to introduce this product if the mean sales per store are more than $600 per week. In a marketing test the product is sold at 26 stores. From the sample it is found that the mean for weekly sales is $603.20 and the standard deviation is $60. a. State the null and alternative hypotheses b. Carry out the test and give the P-value. Report your conclusion. c. Is the result significant at the 5% level? d. Give a 95% confidence interval for the mean sales.