Question

Businesses know that customers often respond to background music. Do they also respond to odors? One study of this question took place in a small pizza restaurant in France on two Saturday evenings in May. On one of these evenings, a relaxing lavender odor was spread through the restaurant. On the other evening no scent was used. The data gives the time, in minutes, that two samples of 30 customers spent in the restaurant and the amount they spent in euros. No odor Lavender Minutes Euros spent Minutes Euros spent 103 15.9 92 21.9 68 18.5 126 18.5 79 15.9 114 22.3 106 18.5 106 21.9 72 18.5 89 18.5 121 21.9 137 24.9 92 15.9 93 18.5 84 15.9 76 22.5 72 15.9 98 21.5 92 15.9 108 21.9 85 15.9 124 21.5 69 18.5 105 18.5 73 18.5 129 25.5 87 18.5 103 18.5 109 20.5 107 18.5 115 18.5 109 21.9 91 18.5 94 18.5 84 15.9 105 18.5 76 15.9 102 24.9 96 15.9 108 21.9 107 18.5 95 25.9 98 18.5 121 21.9 92 15.9 109 18.5 107 18.5 104 18.5 93 15.9 116 22.8 118 18.5 88 18.5 87 15.9 109 21.9 101 25.5 97 20.7 75 12.9 101 21.9 86 15.9 106 22.5 To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt! The two evenings were comparable in many ways (weather, customer count, and so on), so we are willing to regard the data as independent SRSs from spring Saturday evenings at this restaurant. The authors say, "Therefore, at this stage it would be impossible to generalize the results to other restaurants." (a) Does a lavender odor encourage customers to stay longer in the restaurant? Examine the time data and explain why they are suitable for two‑sample ? procedures. Because the distributions are reasonably symmetric with no outliers and the samples can be treated as independent SRSs, the ? procedures will work well. false true Let ?1 be the population mean time in the restaurant with no scent, and ?2 be the mean time with a lavender odor. State the null and alternative hypotheses. ?0:?1=?2 vs. ??:?1>?2 ?0:?1=?2 vs. ??:?1<?2 ?0:?1>?2 vs. ??:?1<?2 ?0:?1=?2 vs. ??:?1≠?2 Give the value of the test statistic. (Enter your answer rounded to two decimal places.) test statistic: Use the conservative degrees of freedom to give the P‑value for the test. 0.01<?<0.02 0.0005<?<0.001 ?<0.0005 0.0025<?<0.005 What is your conclusion? We have sufficient evidence that customers stay longer when there is no odor. There is no evidence that the mean time spent in the restaurant when lavender odor is present is different from the mean time spent when there is no odor. We have some evidence that the mean times spent when lavender odor is present and when there is no odor are not the same. We have strong evidence that customers stay longer when the lavender odor is present. (b) Does a lavender odor encourage customers to spend more while in the restaurant? Examine the spending data. In what ways do these data deviate from normality? Select your choices. There are extreme outliers. The distributions do not have similar shapes. The distributions are skewed and have many gaps. There are two clear asymmetrical peaks in each distribution. If ?1 is the population mean spending with no scent, and ?2 is the mean spending with a lavender odor, what are the null and alternative hypotheses? ?0:?1=?2 versus ??:?1<?2 ?0:?1−?2=0 versus ??:?1−?2>0 ?0:?1=?2 versus ??:?1≠?2 ?0:?1=?2 versus ??:?1>?2 Give the value of the test statistic. (Enter your answer rounded to two decimal places.) test statistic: What is the P‑value? ?<0.0005 0.0025<?<0.005 0.0005<?<0.001 0.01<?<0.02 What is your conclusion? We have strong evidence that customers spend more when the lavender odor is present. We have some evidence that mean spending is larger when the lavender odor is present. We have strong evidence that the presence of lavender odor has no effect on the spendings of customers. The data is not sufficient to give evidence against the null hypothesis of no difference in spendings.

Answer 1

a. We suspect in advance that the lavender odors encourage customers to spend more time (Min) that that of No Odor, so the alternative is two sided.

Using Minitab:

Step 1: Click Stat → Basic Statistics → 2-Sample t.

Step 2: Click in the blank box next to “MinNo” and the “MinLave” appears in the list box on the left.

Check the box that says “Assume Equal Variances”

Click “OK” to save, and click “OK” again to run the test.

Results of our 2-Sample t Test:

P-value is 0.000 . Data give very strong evidence (P-value < 0.05) that lavender oder encourages customers to stay longer in the restaurant.

Part b.

Here we have to examine the data that there is no statistical significant difference between averages spending by the customers in the restaurant, so alternative is two sided.

We use same steps as above with changing alternative two tailed.

Minitab Output:

P-value < 0.0005 The data give strong evidence that to conclude that the Lavender odor encourages customer to spent more time in restaurant.

Hope this will helps you. Thanks and God Bless You :)