Question

A report just came out that stated that 23.6% of all Americans say that vanilla is their favorite ice cream, 23.8% say that chocolate is their favorite, 9.7% favor butter pecan, 9% favor strawberry, and the rest have other favorites. An ice cream shop owner thinks that her customers are not like the rest of America. The table below shows the results of 970 of her patrons' ice cream selections. What can be concluded at the a = 0.05 significance level? a. Complete the table by filling in the expected frequencies. Round your answers to the nearest whole number Frequencies of Favorite Ice Cream Outcome Frequency Expected Frequency Vanilla 210 Chocolate 219 Butter Pecan 92 Strawberry 101 Other 348 b. What is the correct statistical test to use? Select an answer c. What are the null and alternative hypotheses? Ho: O Favorite ice cream and where the ice cream is purchased are dependent. O The distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general. The distribution of favorite ice cream for customers at her shop is not the same as it is for Americans in general. O Favorite ice cream and where the ice cream is purchased are independent.

Answer 1

(a)

Data	Observed values (fo)	Expected Proportions	Expected values (fe)
vanilla	210	0.236	228.92
chocolate	219	0.238	230.86
butter pecan	92	0.097	94.09
strawberry	101	0.090	87.30
other	348	0.339	328.83
Total	970	1.000	970.00

(b) Chi square test for Goodness of Fit

(c) Ho: The distribution of favorite ice cream for customers at her shop is the same as it is for Amercians in general.

(d) Ho: The distribution of favorite ice cream for customers at her shop is not same as it is for Amercians in general.

(e) Test statistics

Data	Observed values (fo)	Expected Proportions	Expected values (fe)	(fo-fe)2/ fe
vanilla	210	0.236	228.92	1.564
chocolate	219	0.238	230.86	0.609
butter pecan	92	0.097	94.09	0.046
strawberry	101	0.090	87.30	2.150
other	348	0.339	328.83	1.118
Total	970	1.000	970.00	5.487

$\chi^{2}$ = 5.487

(f) p value = 0.2409

(g) p value is greater than alpha

(h) Based on this, we should not reject null hypothesis. (fail to reject Ho)

(i) There is insufficient evidence to conclude that the distribution of fav ice cream for customer in her shop is not the smae as it is for Americans in general.