11. Use the following information for questions 27 to 29. The general manager of
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Question
11. Use the following information for questions 27 to 29. The general manager of the Nordstrom store in Novi wants to see if the financial crisis had an impact on the average amount a customer spent in the store in 2009. A random sample of 29 customers (n1) was surveyed in July of 2008 and the average amount of money spent was $415 with a variance of 5.43. In July of 2009, a random sample of 45 customers (n2) spent an average amount of $412 with a variance of 7.11. Based on these data, is there evidence that the average amount spent per customer was smaller in 2009 than in 2008? Use alpha = .05.
(1) What is the correct critical value for this test? 1.658 1.671 1.960 1.980 2.000
(2) What is the calculated value for this test? -5.11 -4.96 1.67 4.96 5.11
(3) What is the correct managerial decision for this scenario? The average amount spent per customer in 2009 was less than or equal to the amount spent in 2008. The average amount spent per customer in 2009 was greater than or equal to the amount spent in 2008. The average amount spent per customer in 2009 was less than the average amount spent in 2008. (4) (4) Reject the null hypothesis.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 2008> 2009
Alternative hypothesis: 2008 < 2009
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees offreedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.5876
DF = 72
t = [ (x1 - x2) - d ] / SE
t = 5.11
tcritical = 1.67
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
Interpret results. Since the t-value (5.11) is greater than the t critical(1.67), hence we have to reject the null hypothesis.
The average amount spent per customer in 2009 was less than the average amount spent in 2008.
Reject the null hypothesis.
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