1 answer

A report just came out that stated that 23.6% of all Americans say that vanilla is...

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 c
H: The distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general The distrib
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.
H: 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. Favorite ice cream and where the ice cream is purchased are independent. Favorite ice cream and where the ice cream is purchased are dependent. d. The degrees of freedom e. The test-statistic for this data (Please show your answer to three decimal places.) f. The p-value for this sample= (Please show your answer to four decimal places.) g. The p-value is Select an answer va h. Based on this, we should Select an answer i. Thus, the final conclusion is... There is sufficient evidence to conclude that favorite ice cream and where the ice cream is purchased are dependent. There is sufficient evidence to conclude that the distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general. There is insufficient evidence to conclude that favorite ice cream and where the ice cream is purchased are dependent. There is sufficient evidence to conclude that the distribution of favorite ice cream for customers at her shop is not the same as it is for Americans in general. There is insufficient evidence to conclude that the distribution of favorite ice cream for customers at her shop is not the same as it is for Americans in general.

Answers

(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.

.

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