Question

The new manager of a theater plans to offer discounts to increase the number of tickets sold for shows on Monday and Tuesday evenings. She uses a sample of 30 weeks to record the number of tickets sold on these two days. A portion of the data is shown in the accompanying table.  

Monday	Tuesday
221	208
187	199
272	175
199	196
235	205
221	202
227	204
228	196
183	202
236	197
238	190
191	196
210	173
220	193
222	191
245	212
223	169
211	180
226	187
239	173
264	196
207	184
230	193
207	197
204	173
253	181
223	174
230	182
225	194
194	180

a) Using excel Produce a 95% CI for the mean number of tickets sold for shows on Monday evening, using the format discussed in class. The dataset descriptions for this question may be inadequate. As you answer this question 'warn" about important missing information in your conditions assessment. Once you have completed your conditions assessment clearly list any assumptions that need to be made. After you list the required assumptions – if any - presume that everything is OK, and answer the rest of the question.

b) Is there any evidence that the population mean differs from 200 for shows on Monday evenings?

Answer 1

a) We assume that the distribution is approximately normal.

if the sample size is large , then the sampling distribution will be approximately normal

b)

Test statistic:

Since the P-value is less than the significance level , we shall reject the null hypothesis. Thus we have evidence that the population mean differs from 200 for shows on Monday evenings.