A company attempts to evaluate the potential for a new bonus plan and decides to use the bonus plan for a trial period. The weekly sales volume achieved by a sample of 4 salespersons before and after implementing the bonus plan is shown below. (For the following matched samples, let the difference d = After - Before.) Weekly Sales (in units) Salesperson Before After 1 48 44 2 48 40 3 38 36 4 44 50 Assume the population of differences is normally distributed. a. State the hypotheses. b. Compute the test statistic. c. Use α = .05 and test to see if the bonus plan will result in an increase in the mean weekly sales for the company.
Added by Eric E.
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H0: μd = 0 - Alternative Hypothesis (Ha): The mean difference in weekly sales before and after implementing the bonus plan is not zero. Ha: μd ≠0 ** Show more…
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A company attempts to evaluate the potential for a new bonus plan by selecting a sample of 4 salespersons to use the bonus plan for a trial period. The weekly sales volume before and after implementing the bonus plan is shown below. (For the following matched samples, let the difference "d" be d = after - before.) Use Alpha = .05 and test to see if the bonus plan will result in an increase in the mean weekly sales. 1. State the null and alternative hypotheses to be tested 2. Identify the test statistics 3. Determine the critical value(s) for this test and formulate a decision rule. (please round three decimal places) 4. Find the mean for the difference 5. Find the standard deviation for the difference 6. Compute the test statistic
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A corporation administers an aptitude test to all new sales representatives. Management is interested in the extent to which this test is able to predict weekly sales of new representatives. Aptitude test scores range from 0 to 30 with greater scores indicating a higher aptitude. Weekly sales are recorded in hundreds of dollars for a random sample of 10 representatives. Test scores and weekly sales are as follows: $$ \begin{array}{lllllllllll} \hline \text { Test Score, } x & 12 & 30 & 15 & 24 & 14 & 18 & 28 & 26 & 19 & 27 \\ \hline \text { Weekly Sales, } y & 20 & 60 & 27 & 50 & 21 & 30 & 61 & 54 & 32 & 57 \\ \hline \end{array} $$ a. Compute the covariance between test score and weekly sales. b. Compute the correlation between test score and weekly sales.
A commercial farmer harvests his entire field of a vegetable crop at one time. Therefore, he would like to plant a variety of green beans that mature all at one time (small standard deviation between maturity times of individual plants). A seed company has developed a new hybrid strain of green beans that it believes to be better for the commercial farmer. The maturity time of the standard variety has an average of 50 days and a standard deviation of 2.1 days. A random sample of 30 plants of the new hybrid showed a standard deviation of 1.65 days. Does this sample show a significant lowering of the standard deviation at the 0.05 level of significance? Assume that maturity time is normally distributed. a. Solve using the $p$ -value approach. b. Solve using the classical approach.
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