Math 2311 EMCF Homework 12 Sections 8.3 - 8.4 Honework will NOT be accepted through email or in person. Homework must be submitted through CourseWare, https://www.casa.uh.edu, before the deadline. Submit this assignment on CourseWare under \"EMCF\" and choose ehw12. 1. The choice between a z-test and a t-test for a population mean depends primarily on: a. b. c. d. e. the sample size. the level of significance. whether a one- or two-tailed test is indicated. whether the given standard deviation is from the population or the sample. a z-test should never be used. 2. The p-value of a test of significance is the probability that: a. b. c. d. e. the decision resulting from the test is correct. 95% of the confidence intervals will contain the parameter of interest. the null hypothesis is true. the alternative hypothesis is true. None of these describes the p-value. 3. If we want to claim that a population parameter is different from a specified value, this situation can be considered as a two-tailed test. a. True b. False 4. In the p-value approach to hypothesis testing, if the p-value is less than a specified significance level, we fail to reject the null hypothesis. a. True b. False 5. To use the matched-pairs t procedure to perform a significance test on two samples, we assume a. b. c. d. e. The populations' standard deviations are known. The samples from each population are dependent. The distributions are exactly normal in each population. The sample sizes are large. None of the above. 1 6. The manager of a factory wants to compare the mean number of units assembled per employee in a week for two new assembly techniques. Two hundred employees from the factory are randomly selected and each is randomly assigned to one of the two techniques. After teaching 100 employees one technique and 100 employees the other technique, the manager records the number of units each of the employees assembles in one week. Which of the following would be the most appropriate inferential statistical test in this situation? a. b. c. d. e. One-sample z-test Two-sample t-test Matched Pairs t-test Chi-square goodness-of-fit test One-sample t-test 7. Do you have an insatiable craving for chocolate or some other food? Since many North Americans apparently do, psychologists are designing scientific studies to examine the phenomenon. According to the New York Times (Feb. 22, 1995), one of the largest studies of food cravings involved a survey of 1000 McMaster University (Canada) students. The survey revealed that 97% of the women in the study acknowledged specific food cravings while only 67% of the men did. Assume that 600 of the respondents were women and 400 were men. Is there sufficient evidence to claim that the true proportion of women who acknowledge having food cravings exceed the corresponding proportion for men? a. No. Since the p-value is so large, there is no statistical evidence to reject the null hypothesis of no difference in population proportion of food cravings based on gender. b. Yes. Since the p-value is so small, there is statistical evidence to reject the null hypothesis of no difference between gender population proportions of food cravings. c. The sample size is insufficient to perform a hypothesis test. d. No. Since the p-value is greater than alpha (0.05), there is no statistical evidence to reject the null hypothesis of population proportion women food cravings is greater than men food cravings. e. Yes. Since the p-value is less than alpha (0.05), there is statistical evidence to reject the alternative hypothesis that population proportion of women food cravings is larger than men food cravings. 8. We wish to test if a new feed increases the mean weight gain compared to an old feed. At the conclusion of the experiment it was found that the new feed gave a 10 kg bigger gain than the old feed. A two-sample t-test with the proper one-sided alternative was done and the resulting p-value was .082. This means: a. there is an 8.2% chance the null hypothesis is false. b. there was only an 8.2% chance of observing an increase greater than 10 kg (assuming the null hypothesis was true). c. there was only an 8.2% chance of observing an increase greater than 10 kg (assuming the null hypothesis was false). d. there is an 8.2% chance the alternate hypothesis is true. e. there is only an 8.2% chance of getting a 10 kg increase. 2 For questions 9 and 10, use the following information: A random sample of 288 voters registered in the state of California showed that 141 voted in the last general election. A random sample of 216 registered voters in the state of Colorado showed that 125 voted in the most recent general election. 9. Which of the following is the correct condition that allows us to calculate the standard deviation? a. There are at least 2880 registered voters in California and at least 2160 registered voters in Colorado. b. 288(.49), 288(.51), 216(.58), and 216(.42) are all greater than 10. c. 288(.53), 288(.47), 216(.53), and 216(.47) are all greater than 10. d. There are at least 5040 registered voters in the U.S. e. We cannot calculate a standard deviation since this problem involves proportions. 10. The absolute value of the appropriate test statistic for testing the claim that more registered voters in Colorado voted in the last general election than those in California is a. b. c. d. e. t = 1.98 z = 4.87 z = 1.98 p = .0237 none of these 11. Herbicide A has been used for years in order to kill a particular type of weed, but an experiment is to be conducted in order to see whether a new herbicide, Herbicide B, is more effective than Herbicide A. Herbicide A will continue to be used unless there is sufficient evidence that Herbicide B is more effective. The alternative hypothesis in this problem is that a. b. c. d. e. Herbicide A is more effective than Herbicide B. Herbicide B is more effective than Herbicide A. Herbicide A is not more effective than Herbicide B. Herbicide B is not more effective than Herbicide A. Herbicides A and B differ in effectiveness. 3 For questions 12-15: We want to compare the cost of three and four bedroom home. The following information is an output R comparing the mean list price of a four bedroom house to the mean list price of a three bedroom home. ``` ## ## Welch Two Sample t-test ## ## data: bed4 and bed3 ## t = 1.5526, df = 27.094, p-value = 0.1321 ## alternative hypothesis: true difference in means is not equal to 0 ## 95 percent confidence interval: ## -14593.88 105438.33 ## sample estimates: ## mean of x mean of y ## 284266.7 238844.4 ``` 12. We want to know if there is a difference between the mean list price of a three bedroom home, 3 , and the mean list price of a four bedroom home, 4 . What is the alternative hypothesis? a. b. c. d. e. 4 = 3 x 4 6= x 3 4 6= 3 4 > 3 x 4 > x 3 13. Give the test statistic of this test. a. b. c. d. e. 1.5526 27.094 0.1321 -14593.88 105438.33 14. Give the p-value of this test. a. b. c. d. e. 1.5526 27.094 0.1321 -14593.88 105438.33 4 15. Which is the proper conculsion of this hypothesis test? a. We reject the null hypothesis at 5% significance. There is extremely strong evidence of a significance difference between the mean list price of three bedroom homes and the mean list price of four bedroom homes. b. We reject the null hypothesis at 5% significance. There is no evidence of a significance difference between the mean list price of three bedroom homes and the mean list price of four bedroom homes. c. We fail to reject the null hypothesis at 5% significance. There is no evidence of a significance difference between the mean list price of three bedroom homes and the mean list price of four bedroom homes. d. We fail reject the null hypothesis at 5% significance. There is extremely strong evidence of a significance difference between the mean list price of three bedroom homes and the mean list price of four bedroom homes. e. We accept the null hypothesis at 5% significance. There is extremely strong evidence of a significance difference between the mean list price of three bedroom homes and the mean list price of four bedroom homes. 5