Businesses know that customers often respond to backgroundmusic. Do they also respond to odors? One study of this questiontook place in a small pizza restaurant in France on two Saturdayevenings in May. On one of these evenings, a relaxing lavender odorwas spread through the restaurant. On the other evening no scentwas used. The data gives the time, in minutes, that two samples of30 customers spent in the restaurant and the amount they spent ineuros. No odor Lavender Minutes Euros spent Minutes Euros spent 10315.9 92 21.9 68 18.5 126 18.5 79 15.9 114 22.3 106 18.5 106 21.9 7218.5 89 18.5 121 21.9 137 24.9 92 15.9 93 18.5 84 15.9 76 22.5 7215.9 98 21.5 92 15.9 108 21.9 85 15.9 124 21.5 69 18.5 105 18.5 7318.5 129 25.5 87 18.5 103 18.5 109 20.5 107 18.5 115 18.5 109 21.991 18.5 94 18.5 84 15.9 105 18.5 76 15.9 102 24.9 96 15.9 108 21.9107 18.5 95 25.9 98 18.5 121 21.9 92 15.9 109 18.5 107 18.5 10418.5 93 15.9 116 22.8 118 18.5 88 18.5 87 15.9 109 21.9 101 25.5 9720.7 75 12.9 101 21.9 86 15.9 106 22.5 To access the complete dataset, click the link for your preferred software format: ExcelMinitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt! The two eveningswere comparable in many ways (weather, customer count, and so on),so we are willing to regard the data as independent SRSs fromspring Saturday evenings at this restaurant. The authors say,"Therefore, at this stage it would be impossible to generalize theresults to other restaurants." (a) Does a lavender odor encouragecustomers to stay longer in the restaurant? Examine the time dataand explain why they are suitable for two?sample ? procedures.Because the distributions are reasonably symmetric with no outliersand the samples can be treated as independent SRSs, the ?procedures will work well. false true Let ?1 be the population meantime in the restaurant with no scent, and ?2 be the mean time witha lavender odor. State the null and alternative hypotheses.?0:?1=?2 vs. ??:?1>?2 ?0:?1=?2 vs. ??:?1?2 vs.??:?10 ?0:?1=?2 versus ??:?1??2 ?0:?1=?2versus ??:?1>?2 Give the value of the test statistic. (Enteryour answer rounded to two decimal places.) test statistic: What isthe P?value? ?<0.0005 0.0025
