A report just came out that stated that 24.2%  of all Americans say that vanilla is their favorite ice cream,  23.9% say that chocolate is their favorite, 9.4% favor butter pecan, 8.4% 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 885 of her patrons' ice cream selections. What can be concluded at the αα = 0.10 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 203   Chocolate 204   Butter Pecan 65   Strawberry 104   Other 309   What is the correct statistical test to use? Select an answer Homogeneity Independence Goodness-of-Fit Paired t-test  What are the null and alternative hypotheses? H0:H0:  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. 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. 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 independent. 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 Select an answer greater than less than (or equal to)  αα  Based on this, we should Select an answer reject the null fail to reject the null accept the null  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 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 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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 13CYU
icon
Related questions
Topic Video
Question

A report just came out that stated that 24.2%  of all Americans say that vanilla is their favorite ice cream,  23.9% say that chocolate is their favorite, 9.4% favor butter pecan, 8.4% 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 885 of her patrons' ice cream selections. What can be concluded at the αα = 0.10 significance level?

  1. 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 203

     

    Chocolate 204  
    Butter Pecan 65  
    Strawberry 104  
    Other 309  
  2. What is the correct statistical test to use?
    Select an answer Homogeneity Independence Goodness-of-Fit Paired t-test 
  3. What are the null and alternative hypotheses?
    H0:H0: 
    • 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.
    • 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.

    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 independent.
    • 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.) 

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

  8. Based on this, we should Select an answer reject the null fail to reject the null accept the null 
  9. 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 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 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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Proportions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax