TRSP 603 1. A company has been successfully manufacturing aircraft altimeters with errors that have a standard deviation of 43.7ft. After installing new production equipment, 30 altimeters are randomly selected from the new line. This sample group has errors with a standard deviation of 54.7ft. At the 5% level of significance, test that the new population has errors with a standard deviation equal to 43.7ft. 2. A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. The standard deviation of the population (?) is known to be 5.6 days. a. State the null and alternative hypotheses. b. Using the critical value approach, test to determine if their advertisement is legitimate. Let ? = .05. c. Using the p-value approach, test the hypotheses at the 5% level of significance. 3. Nancy believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and the following running times were obtained. Assume the population of the running times is normally distributed. 150 150 180 170 a. Compute the sample mean and the standard deviation. b. State the null and alternative hypotheses. c. Using the critical value approach, test the hypotheses at the 10% level of significance. d. Using the p-value approach, test the hypotheses at the 10% level of significance. e. Compute the probability of a Type II error if the true running time of movies equals 130 minutes. 4. Consider the following hypothesis test: Ho: P ? 0.8 Ha: P > 0.8 A sample of 400 provided a sample proportion of 0.853. a. Determine the standard error of the proportion. b. Compute the value of the test statistic. c. Determine the p-value; and at 95% confidence, test the above hypotheses. 5. There are 500 employees in a firm, 45% are female. A sample of 60 employees is selected randomly. a. Determine the standard error of the proportion. b. What is the probability that the sample proportion (proportion of females) is between 0.40 and 0.55?
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