2. The management of Danone Dogal is concerned about the number of boxes of fruit yoghurt they will sell to newly recruited retailers. They want to find out whether the new retailers are more likely to buy more than 185 boxes in a month than existing retailers. 50% of all existing retaliers purchase more than 185 boxes of fruit yoghurt from Danone Dogal in a month.

During the past month, 49 of the new retailers were randomly sampled and the number of boxes of fruit yoghurt purchased by each of the sampled retailers is listed as follows:

180, 155, 202, 133, 125, 230, 124, 136, 240, 138, 149, 225, 126, 232, 224, 190, 201,

182, 221, 195, 187, 226, 167, 189, 146, 205, 203, 194, 168, 214, 218, 183, 135, 156,

152, 201, 190, 168, 198, 182, 205, 191, 175, 193, 182, 223, 207, 188, 179.

A hypothesis test is to be carried out.

(a) What is the observed proportion of new retailers who purchased more than 185 boxes?

(b) State the null and the alternative hypotheses of the hypothesis test. Dene all your notation.

(c) Compute the test statistic based on the collected data. State all the assumptions you need to carry out the test.

(d) Compute the P-value. Sketch your model and shade the corresponding area.

(e) At the 5% signicance level, state your conclusion in the context of this question.