Statistic for Business BBUS - Exercise_Session 8

Session 8. One-sample hypothesis testing S8.1 A manufacturer claims that the average life of their electric light bulbs is 2000 hours. A random sample of 64 bulbs is tested and the life, x, in hours, is recorded. The results obtained are as follows: Is there sufficient evidence, at the 1% level, that the manufacturer is over-estimating the length of the life of the light bulbs? S8.2 People who diet can expect to lose an average of 3 kg in a month. In a book, the authors claim that people who follow a new diet will lose an average of more than 3 kg in a month. The weight losses of the 180 people in a random sample who had followed the new diet for a month were noted. The mean was 3.3 kg, and the standard deviation was 2.8 kg. Test the authors’ claim at the 5% significance level. S8.3 In a sample of 402 UEH students, 174 are enrolled in Accounting courses. a. Calculate the sample proportion. b. Is the proportion of students enrolled in Accounting courses in the population of all UEH students different from 0.50 at the significance level α = 0.05? c. Find the p-value for the test in B and confirm the result in (b). S8.4 Empirical research shows that the average time for breakfast is 3.10 minutes. After an initiative to help increase the time for breakfast, a researcher randomly samples 20 persons and finds that the average time of the sample is 3.18 with a sample standard deviation of 0.54. Please test the hypothesis that the average time for breakfast is different from 3.10 minutes at a 5% significance level. S8.5 A report from the credit department indicates credit growth from 36 branches of a commercial bank yields a sample mean of 7.2%. It is known that the standard deviation of the population of all branches is 2.5%. A manager does not believe the report because he has seen a significant improvement in the credit market, compared to the 7% of last year. a. Test the null hypothesis at the 5% significance level. State the conclusion in terms of the problem. b. Calculate the p-value and test against your hypothesis at 10%, 15% significance level. S8.6 Twelve cities in Vietnam are randomly sampled to collect the data about monthly rainfall, in centimeters. The detailed data is as follows 222, 188, 252, 210, 202, 193, 198, 219, 202, 156, 184, 232 Assume that monthly rainfalls follow the normal distribution. Test the null hypothesis that the mean monthly rainfall of all cities in Vietnam is 200. a. Use a right-sided test at 1% significance level b. Use a two-sided test at 5% significance level. State the conclusion in terms of the problem. S8.7 The owner of a specialty coffee shop wants to study coffee purchasing habits of customers at her shop. She selects a random sample of 60 customers during a certain week, with the following results: ·The amount spent was $7.25, standard deviation was $1.75. · Thirty-one customers say they “definitely will” recommend the specialty coffee shop to family and friends. a. At the 0.05 level of significance, is there evidence that the population mean amount spent was different from $6.50? b. Determine the p-value in (a). c. At the 0.05 level of significance, is there evidence that more than 50% of all the customers say they “definitely will” recommend the specialty coffee shop to family and friends? d. What is your answer to (a) if the sample mean equals $6.25? e. What is your answer to (c) if 39 customers say they “definitely will” recommend the specialty coffee shop to family and friends?