A report just came out that stated that 21.7% of all Americans say that vanilla is their favorite ice cream, 20.3% say that chocolate is their favorite, 8.9% favor butter pecan, 9.6% 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 820 of her patrons' ice cream selections. What can be concluded at the αα = 0.01 significance level?Complete the table by filling in the expected frequencies. Round your answers to the nearest whole number.Frequencies of Favorite Ice CreamOutcomeFrequencyExpected FrequencyVanilla168Incorrect Chocolate176Incorrect Butter Pecan45Incorrect Strawberry93IncorrectOther338IncorrectWhat is the correct statistical test to use?Select an answer Goodness-of-Fit Homogeneity Paired t-test Independence CorrectWhat are the null and alternative hypotheses?H0:H0: The distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general.Favorite ice cream and where the ice cream is purchased are independent.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 dependent.CorrectH1:H1: 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 dependent.Favorite ice cream and where the ice cream is purchased are independent.CorrectThe degrees of freedom = CorrectThe test-statistic for this data = Incorrect (Please show your answer to three decimal places.)The p-value for this sample = Incorrect(Please show your answer to four decimal places.) The p-value is Select an answer greater than less than (or equal to) Correct αα Based on this, we should Select an answer fail to reject the null reject the null accept the null

1. The expected frequencies are, Outcome Frequency Expected frequency Vanilla 168 820×0.217=178 Chocolate 176 820×0.203=166 Butter Pecan 45 820×0.089=73 Strawberry 93 820×0.096=79 Other 338 820×0.395=324 Total 820 820 2. The chi-square is a non-parametric test which is used for comparing the categorical variables. The chi-square goodness of fit test helps in determining how the observed distribution fits the expected distribution. It is used for comparing the observed data with the expected data. The variables favorite ice cream is categorical variable. The chi-square goodness of fit test can be used for comparing the observed data with the expected frequencies. Correct answer: Goodness-of-Fit Homogeneity.3. The hypothesis is, Null hypothesis: H0: The distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general. Alternative hypothesis: H1: The distribution of favorite ice cream for customers at her shop is not the same as it is for Americans in general. 4. The degrees of freedom is, df=k-1=5-1=4 Thus, the degrees of freedom is 4. 5. The test statistic is, χ2=Sum ofObserved-Expected2Expected=168-1782178+176-1662166+45-73273+93-79279+338-3242324=0.5618+0.6024+10.7397+2.4810+0.6049=14.9898≈14.990 Thus, the test statistic is 14.990. 6. Computation of p-value: The p-value of χ2-distribution for test statistic 14.990 at 4 degrees of freedom can be obtained using the excel formula “=CHISQ.DIST.RT(14.990,4)”. The p-value is 0.0047. Thus, the p-value is 0.0047. 7. Decision rule: If p-value≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: The p-value (0.0047) is less than the level of significance (0.01). 8. Based on decision rule, reject the null hypothesis. Thus, it can be concluded that the distribution of favorite ice cream for customers at her shop is not the same as it is for Americans in general.

Answered: A report just came out that stated that…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A report just came out that stated that 21.7% of all Americans say that vanilla is their favorite ice cream, 20.3% say that chocolate is their favorite, 8.9% favor butter pecan, 9.6% 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 820 of her patrons' ice cream selections. What can be concluded at the αα = 0.01 significance level?

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 168
Incorrect

Chocolate 176 Incorrect

Butter Pecan 45 Incorrect

Strawberry 93 Incorrect

Other 338 Incorrect
What is the correct statistical test to use?
Select an answer Goodness-of-Fit Homogeneity Paired t-test Independence Correct
What are the null and alternative hypotheses?
H0:H0:
- The distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general.
- Favorite ice cream and where the ice cream is purchased are independent.
- 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 dependent.
Correct
H1:H1:
- 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 dependent.
- Favorite ice cream and where the ice cream is purchased are independent.
Correct
The degrees of freedom = Correct
The test-statistic for this data = Incorrect (Please show your answer to three decimal places.)
The p-value for this sample = Incorrect(Please show your answer to four decimal places.)
The p-value is Select an answer greater than less than (or equal to) Correct αα
Based on this, we should Select an answer fail to reject the null reject the null accept the null

Outcome	Frequency	Expected Frequency
Vanilla	168	Incorrect
Chocolate	176	Incorrect
Butter Pecan	45	Incorrect
Strawberry	93	Incorrect
Other	338	Incorrect

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