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 m

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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 3030 customers spent in the restaurant and the amount they spent in euros.

No odor Lavender
Minutes Euros spent Minutes Euros spent
103103 15.915.9 9292 21.921.9
6868 18.518.5 126126 18.518.5
7979 15.915.9 114114 22.322.3
106106 18.518.5 106106 21.921.9
7272 18.518.5 8989 18.518.5
121121 21.921.9 137137 24.924.9
9292 15.915.9 9393 18.518.5
8484 15.915.9 7676 22.522.5
7272 15.915.9 9898 21.521.5
9292 15.915.9 108108 21.921.9
8585 15.915.9 124124 21.521.5
6969 18.518.5 105105 18.518.5
7373 18.518.5 129129 25.525.5
8787 18.518.5 103103 18.518.5
109109 20.520.5 107107 18.518.5
115115 18.518.5 109109 21.921.9
9191 18.518.5 9494 18.518.5
8484 15.915.9 105105 18.518.5
7676 15.915.9 102102 24.924.9
9696 15.915.9 108108 21.921.9
107107 18.518.5 9595 25.925.9
9898 18.518.5 121121 21.921.9
9292 15.915.9 109109 18.518.5
107107 18.518.5 104104 18.518.5
9393 15.915.9 116116 22.822.8
118118 18.518.5 8888 18.518.5
8787 15.915.9 109109 21.921.9
101101 25.525.5 9797 20.720.7
7575 12.912.9 101101 21.921.9
8686 15.915.9 106106 22.522.5

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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 ?t procedures.
Because the distributions are reasonably symmetric with no outliers and the samples can be treated as independent SRSs, the ?t procedures will work well.
true
false
Let ?1μ1 be the population mean time in the restaurant with no scent, and ?2μ2 be the mean time with a lavender odor. State the null and alternative hypotheses.
?0:?1>?2H0:μ1>μ2 vs. ??:?1<?2Ha:μ1<μ2
?0:?1=?2H0:μ1=μ2 vs. ??:?1>?2Ha:μ1>μ2
?0:?1=?2H0:μ1=μ2 vs. ??:?1<?2Ha:μ1<μ2
?0:?1=?2H0:μ1=μ2 vs. ??:?1≠?2Ha:μ1≠μ2
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.
0.0005<?<0.0010.0005<P<0.001
?<0.0005P<0.0005
0.0025<?<0.0050.0025<P<0.005
0.01<?<0.020.01<P<0.02
What is your conclusion?
We have some evidence that the mean times spent when lavender odor is present and when there is no odor are not the same.
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 strong evidence that customers stay longer when the lavender odor is present.
We have sufficient evidence that customers stay longer when there is no odor.
(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.
The distributions do not have similar shapes.
There are two clear asymmetrical peaks in each distribution.
The distributions are skewed and have many gaps.
There are extreme outliers.
If ?1μ1 is the population mean spending with no scent, and ?2μ2 is the mean spending with a lavender odor, what are the null and alternative hypotheses?
?0:?1=?2H0:μ1=μ2 versus ??:?1≠?2Ha:μ1≠μ2
?0:?1−?2=0H0:μ1−μ2=0 versus ??:?1−?2>0Ha:μ1−μ2>0
?0:?1=?2H0:μ1=μ2 versus ??:?1>?2Ha:μ1>μ2
?0:?1=?2H0:μ1=μ2 versus ??:?1<?2
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