BNAD 276: Stats Inference in Management Fall 2017 - Dr. Suzanne Delaney Homework 17 - Hypothesis Testing with z and t-scores Name CID #: This homework contains three problems that will allow you to help in making decisions using hypothesis testing. Please note there is a t-table at the back of this packet. Please show your work (write small and neat). 1. This is a \"quality control\" problem. Your grocery store sells 5-pound bags of whole potatoes. You know that there will be variability; some bags will weigh more than others. You also know that you will lose profits if the bags weigh too much, but it would be illegal if the bags weighed too little. The population mean across all stores is 5 pounds and the population standard deviation is 1 pound. You want to know whether the bags of potatoes coming out of a particular plant are too heavy or too light. So you take a sample of 16 bags and you find the average weight of that sample is 6 pounds. You want to know if the 6-pound bags are significantly different from the population mean of 5 pounds ( = .05). Please answer the following questions: a) Would you use a z-test or a t-test for this hypothesis test? (Hint: do you know the population variability?) b) State the null hypothesis and state the alternative hypothesis Null: Alternative: c) Would you use a one-tailed or two-tailed hypothesis test? (Hint: do you want to know about any difference or just a \"less than\" or \"greater than\" sort of difference) d) What would your critical z-score be? e) Calculate your z score: f) Given that your critical z is 1.96 and your observed z is 4.0, describe your decision: Would you reject the null? Is this a significant difference? Is p < 0.05? What is the probability of a Type I error? (Please note the probability of a Type I error = the alpha level.) g) If this were a one-tailed test, what would the critical z score be? Would this have made a difference in terms of our decision? Why? h) If this were a test with alpha of 0.01 (two tailed), what would critical z be? Would it have made a difference in terms of our decision? Why? i) Describe what a Type I and Type II error would be in this case \"Type I error would be concluding concluding when in fact .\" \"Type II error would be when in fact .\" j) You would use a z score of to construct a 95% confidence interval, and a z-score of to construct a 99% confidence interval 2. Your workers in one store appear to be disgruntled and unhappy. You know this because you designed a job-satisfaction questionnaire and gave it to all of your employees, and the mean job-satisfaction score for the whole population was only 85 (out of 100). You're trying to decide whether to hire consultant to affect morale. So, to test whether you should hire her, you send a sample of 16 workers on a weekend retreat with her and when they return they fill out a similar job-satisfaction questionnaire. This sample of 16 workers scored an average of 89 on the questionnaire, with a sample standard deviation of 6. You do not know the standard deviation of the population. You want to know if these workers score differently on job satisfaction than workers in your other stores. You want to test for a significant difference ( = .05). Please answer the following questions: a) Would you use a z-test or a t-test for this hypothesis test? (Hint: do you know the population standard deviation?) b) Would you use a one-tailed or two-tailed hypothesis test? (Hint: do you want to know about any difference or just a \"less than\" or \"greater than\" sort of difference) c) What is your alpha level for this problem? d) What would your degrees of freedom be? e) What would your critical t-score be? f) Calculate your t score: g) Given that your critical t is 2.131, and your observed t is 2.667, describe your decision: Would you reject the null? Is this a significant difference? Is p < 0.05? What is the probability of a Type I error? (Remember, the probability of a Type I error = the alpha level.) h) If this were a one-tailed test, what would the critical t score be? Would this have made a difference in terms of our decision? Why? i) If this were a test with alpha of 0.01 (two tailed), what would critical t be? _ Would it have made a difference in terms of our decision? Why? Would you reject the null? Is this a significant difference? Is p < 0.01? j) Describe what a Type I and Type II error would be in this case \"Type I error would be concluding when in fact .\" \"Type II error would be concluding when in fact .\" k) You would use a t-score of to construct a 95% confidence interval, and a t-score of to construct a 99% confidence interval 3. Mac and Charlie are claiming that their diet will help people lose more weight within a month than is typically lost by people who diet on their own. The typical amount of weight lost is 10 pounds (this is the population mean). Because they are so confident in their diet plan they would like to use a one-tailed test to explore whether their diet is significantly better. So, they take a sample of 18 dieters and record their weight loss one month after joining the program. The sample mean is 12.5 pounds and the sample standard deviation is 9.2 pounds. You want to know if these dieters lose more weight than dieters on their own. You want to test for a significant decline in weight ( = .05). Please answer the following questions: a) Would you use a z-test or a t-test for this hypothesis test? (Hint: do you know the population standard deviation?) b) Would you use a one-tailed or two-tailed hypothesis test? (Hint: do you want to know about any difference or just a \"less than\" or \"greater than\" sort of difference) c) What is your alpha level for this problem? d) What would your degrees of freedom be? e) What would your critical t-score be? f) Calculate your t score: g) Given that your critical t is , and your observed t is , describe your decision: Would you reject the null? Is this a significant difference? Is p < 0.05? What is the probability of a Type I error? h) If this were a two-tailed test, what would the critical t score be? Would this have made a difference in terms of our decision? Why? i) If this were a test with alpha of 0.01 (two tailed), what would critical t be? Would it have made a difference in terms of our decision? Why? Would you reject the null? Is this a significant difference? Is p < 0.01? j) Describe what a Type I and Type II error would be in this case \"Type I error would be concluding when in fact .\" \"Type II error would be concluding when in fact .\" k) You would use a t-score of to construct a 95% confidence interval, and a t-score of to construct a 99% confidence interval For these three summary statements please use the format presented in lecture: Remember, the three parts to the summary are 1. State independent and dependent variables and means for each group 2. Describe type of test, and whether significance was found 3. Finish with the statistical notation to summarize the findings: t(df) = observed t; p< 0.05 (or \"n.s.\") Here is an example from lecture to help you get started. The mean response time for following the sheriff's new plan was 24 minutes, while th Please construct a brief (one paragraph) summary of your results of the \"bags of potato\" problem using this format. Please construct a brief (one paragraph) summary of your results of the \"disgruntled employees\" problem using this format. Please construct a brief (one paragraph) summary of your results of Mac and Charlie's study using this format. t-table for most common critical scores d16s_hw12_z&t_hypothesis_test.docx