A report just came out that stated that 21.2%  of all Americans say that vanilla is their favorite ice cream,  21.9% say that chocolate is their favorite, 8.6% favor butter pecan, 9.2% 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 905 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. Outcome Frequency Expected Frequency Vanilla 188   Chocolate 186   Butter Pecan 97   Strawberry 68   Other 366   What is the correct statistical test to use?      Paired Test, Goodness-of-fit, homogeneity, or independence.  What are the null and alternative hypotheses? H0:H0:  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. 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. H1:H1:  Favorite ice cream and where the ice cream is purchased are independent. 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. 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: greater than or less than/equal to?  Based on this, we should: fail to reject the null, accept the null or 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 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. 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 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.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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A report just came out that stated that 21.2%  of all Americans say that vanilla is their favorite ice cream,  21.9% say that chocolate is their favorite, 8.6% favor butter pecan, 9.2% 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 905 of her patrons' ice cream selections. What can be concluded at the αα = 0.01 significance level?

  1. Complete the table by filling in the expected frequencies.  Round your answers to the nearest whole number.
    Outcome Frequency Expected Frequency
    Vanilla 188

     

    Chocolate 186  
    Butter Pecan 97  
    Strawberry 68  
    Other 366  
  2. What is the correct statistical test to use?
         Paired Test, Goodness-of-fit, homogeneity, or independence. 
  3. What are the null and alternative hypotheses?
    H0:H0: 
    • 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.
    • 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.

    H1:H1: 
    • Favorite ice cream and where the ice cream is purchased are independent.
    • 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.
  4. The degrees of freedom = 
  5. The test-statistic for this data =  (Please show your answer to three decimal places.)
  6. The p-value for this sample = (Please show your answer to four decimal places.) 

The p-value is: greater than or less than/equal to? 

Based on this, we should: fail to reject the null, accept the null or reject the null. 

  1. Thus, the final conclusion is...
    • 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.
    • 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 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.

 

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