Question
Hello, I need help with these questions please. Tub Sales ($) College Degree (1 = Yes) These data are a random sample of the sales
Hello, I need help with these questions please.
Tub Sales ($) | College Degree (1 = Yes) | These data are a random sample of the sales performances (in dollars of tubs sold) of a number of the company's |
107000 | 1 | sales force, along with data on the level of educational attainments (via college degree) of the respective sales people |
87300 | 0 | |
106000 | 1 | |
97700 | 1 | |
108800 | 1 | |
95700 | 0 | |
91200 | 0 | |
119600 | 1 | |
94200 | 0 | |
91300 | 1 | |
85700 | 0 | |
109700 | 1 | |
110400 | 0 | |
90800 | 0 | |
118300 | 1 | |
88500 | 0 | |
88800 | 0 | |
97400 | 1 | |
68500 | 0 | |
106900 | 1 |
3. Refer to the Excel "Tub Sales" data posted on eLearning which considers the sales performance last year of a sample of the Rub-a-Dub company's sales force: (24) Do NOT use the "finite population" corrections for standard deviation calculation in this problem. Just assume we're dealing with an infinite population. a. Provide the formal null and alternative hypotheses for a hypothesis test of the question of whether or not the mean tub sales is really $93,000. Assume that the underlying population of tub sales is normally distributed. b. Conduct this hypothesis test based on the 90% confidence level (an earlier draft had 'significance' level...that was just an oversight...I mean the typical, alpha = 0.10 case). What is the p-value? Do you reject or fail to reject your null hypothesis from (a)? Why? c. Crea.te a 95% confidence interval for the mean tub sales. Explain in a sentence, in layman's terms, what this confidence interval implies. Would your interval suggest rejecting or failing to reject your null hypothesis from (a) based on this interval (at the 95% level)? Why? d. Compare your conclusions (about rejecting the null hypothesis, or not) in part "b" to part "c". Do these results conflict with each other? (i.e., is it OK to find these two answers simultaneously?...if so, why?...OR, is there a conflict where it should be impossible for these results to occur simultaneously?) e. If I told you that the underlying population of tub sales was NOT normally distributed, how would this change your responses to parts "b" and "c"? f. If I told you that the underlying population of tub sales was NOT normally distributed, BUT, your final calculations (p-value for "b", confidence interval for "c") were based on double the sample size (a sample of 40 salesmen, rather than 20), would this change your response to part "e"? If so, why? If not, why not? You may ignore the above questions and return to the raw "Tub Sales" data. g. The company boasts that at least 70% of its salesmen have college degrees. Provide the formal null and alternative hypotheses for a test of this question. Is this a one or two-tailed hypothesis? h. Do you have a large enough sample to conduct the correct hypothesis test? Explain with a calculation why or why not. (Hint: you need to use a specific rule taken directly from our course slides that fits this scenario's sampling distribution) i. If your answer to part "h" is yes, then conduct this hypothesis test based on the 95% confidence level. Do you reject or fail to reject your null hypothesis? Why?
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