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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Step 1
State the null and alternative hypotheses to be tested: Null Hypothesis (H0): The mean difference in weekly sales volume before and after the bonus plan is equal to zero. This means that the bonus plan has no effect on the weekly sales volume. Alternative Show more…
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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; let population men Before = μ1, population mean After = μ2) 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. State the null and alternative hypotheses. Choose the correct one.
Sri K.
A marketing research firm wishes to compare the prices charged by two supermarket chains—Miller’s and Albert’s. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at 10 of each chain’s stores. The stores for each chain are randomly selected, and all purchases are made during a single week. It is found that the mean and the standard deviation of the shopping expenses at the 10 Miller’s stores are x1 = $130.49 and s1 = 1.02. It is also found that the mean and the standard deviation of the shopping expenses at the 10 Albert’s stores are x2 = $105.92 and s2 = 2.09. (a) Calculate the value of the test statistic. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Test statistic (b) Calculate the critical value. (Round your answer to 2 decimal places.) Critical value (c) At the 0.05 significance level, what it the conclusion? Reject Fail to reject
(a) identify the expected distribution and state $H_{0}$ and $H_{a}$, (b) find the critical value and identify the rejection region, $(c)$ find the chi-square test statistic, $(d)$ decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. A research firm claims that the distribution of the days of the week that people are most likely to order food for delivery is different from the distribution shown in the figure. You randomly select 500 people and record which day of the week each is most likely to order food for delivery. The table shows the results. At $\alpha=0.01,$ test the research firm's claim. (FIGURE CAN'T COPY)
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