Question

In: Statistics and Probability

A report just came out that stated that 22.9% of all Americans say that vanilla is...

A report just came out that stated that 22.9% of all Americans say that vanilla is their favorite ice cream, 23.4% say that chocolate is their favorite, 8% favor butter pecan, 8.7% 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 1000 of her patrons' ice cream selections. What can be concluded at the αα = 0.05 significance level?

Complete the table by filling in the expected frequencies. Round your answers to the nearest whole number.
Frequencies of Favorite Ice Cream

OutcomeFrequencyExpected Frequency

Vanilla243

Chocolate220

Butter Pecan85

Strawberry67

Other385

What is the correct statistical test to use?
Select an answer Paired t-test Homogeneity Independence Goodness-of-Fit

What are the null and alternative hypotheses?
H0:H0:

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.

The distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general.

H1:H1:

The distribution of favorite ice cream for customers at her shop is not the same as it is for Americans in general.

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 dependent.

Favorite ice cream and where the ice cream is purchased are independent.

The degrees of freedom =

The test-statistic for this data = (Please show your answer to three decimal places.)

The p-value for this sample = (Please show your answer to four decimal places.)

The p-value is Select an answer greater than less than (or equal to) αα

Based on this, we should Select an answer reject the null accept the null fail to reject the null

Thus, the final conclusion is...

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.

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 sufficient evidence to conclude that favorite ice cream and where the ice cream is purchased are dependent.

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.

Expert Solution

Ans 1 the correct statistical test to use is
Goodness-of-Fit the null and alternative hypotheses is

H0:The distribution of favorite ice cream for customers at her shop is the same as it is for Americans in general.

H1: The distribution of favorite ice cream for customers at her shop is not the same as it is for Americans in general.

using minitab>Stat>tables>chi square

we have

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: Frequency

Using category names in Ice cream

Test Contribution
Category Observed Proportion Expected to Chi-Sq
vanilla 243 0.229 229 0.85590
chocolate 220 0.234 234 0.83761
butter pecan 85 0.080 80 0.31250
strawberry 67 0.087 87 4.59770
other 385 0.370 370 0.60811

N DF Chi-Sq P-Value
1000 4 7.21181 0.1251

The degrees of freedom =4

The test-statistic for this data = 7.212

The p-value for this sample = 0.1251

The p-value is greater than α

Based on this, we should fail to reject the null

Thus, the final conclusion is...

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.

orchestra answered 1 year ago

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