Question

QUESTION 27 Steve manages inventory for four luxury yacht models sold by his company. Based on a sample of 48 yachts sold over the past few months, he wants to perform a hypothesis test to see if the demand (in terms of the proportion of sales of each model) differs among the four models. His data are as follows: Boat Model Count Windsor Orion otal Use the information above to perform all four steps of the goodness-of-fit test at the α = 0.01 level of significance by filling in the blanks below. 1). Define the hypotheses. Enter proportions, not percentages. Note that the proportions correspond to the categories in the table above from top to bottom. For example, p1 is the null hypothesis proportion for the Windsong" category. Hint: If the demand for each boat type were the same, what would that imply about the proportions of each boat sold? P3 H1: The distribution of boat demand differs among the four models 2). Calculate the test statistic by filling in the table below. Take all calculations toward the final answer two (2) decimal places. Boat Model Observed Count indson Expected Count 12 scope (Observed Expected) Expected 3). Determine the Rejection Regiorn The rejection region is all values of x2» 4). Make a conclusion. We (reject/fail to reject) the null hypothesis. Therefore, we (can/cannot) conclude that the current distribution of property sales has changed from the historical distribution.

Answer 1

Answer Date: 26/03/2019 To test the hypothesis that the distribution of boat demand differs among the four models at 1% significance level. 1) The null and alternative hypothesis is, H, : p -0.25. p? _ 0.25. p.-0.25. p.-0.25 Ha The distributi on of boat demand differs among the four models 2) The chi-square test statistic or goodness-of fit test is, First, find frequency expected then compute chi-square test statistics The average for the observed frequencies computation is the frequencies expected. The total for the expected frequencies must equal for the total observed frequencies. The expected frequencies for Windsong category is,

Total oberved frequency Expected frequency Total number of category 15+11 +10+12 4 If the frequencies are uniformly distributed, the expected frequency is the same for each category and for other boat model categories which are 2 to 4 each has an equal expected frequency which is 12 The chi-square test statistic for goodness-of-fit test is, f. (15-12)2 (11-12)2 (10-12)2 (12-12)2 12 12 12 12 -1.167 The chi-square test statistic for goodness-of-fit test is 1.167 3)

The chi-square critical value is, We need to find degrees of freedom for finding chi-square critical values degrees of freedom -k-1 -4-1 From the critical value table, show degrees of freedom 3 and the significance level 0.01, so the chi-square critical value is 11.345 The chi-square critical value is 11.345 4) Decision The conclusion is that chi-square test statistic for goodness-of-fit test 1.167 less than chi- square critical value 11.345, so the null hypothesis is fail to reject at 1% level of significance. There is insufficient evidence to indicate that the distribution of boat demand differs among the four models. The result is not statistically significant.