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Mitchell works in the produce section at a small local supermarket and would like to test whether the proportion of apples people purchase is the same for each season, using a significance level of 0.025. He analyzes the apple purchases each season for a year and records his findings in the following table. Season # of apples purchased ‒‒‒‒‒‒‒‒‒‒‒‒‒‒ (a) In performing this statistical test, state the hypotheses. O Ho: the distribution of apples people purchased is not the same for each season vs. Ha: the distribution of apples people purchased is the same for each season O Ho: the distribution of apples people purchased is the same for each season vs. Ha: the distribution of apples people purchased is not the same for each season O Ho: the observed number of apples people purchased is the same for each season vs. Ha: the observed number of apples people purchased is not the same for each season O Ho: the total number of apples people purchased is not the same for each season vs. Ha: the total number of apples people purchased is the same for each season O Ho: the proportion of customers is the same each season vs. Ha: the proportion of customers is not the same each season (b) What is the expected number of apples purchased for each season? Fill out the table. (Round your answers to 2 decimal places, if needed.) ....... *‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒ Fall Spring Summer (c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS= (d) The test statistic follows a chi-square distribution with df = 4 Spring 914 (e) Using the statistical table, the p-value is 0.005

Mitchell works in the produce section at a small local supermarket and would like to test whether the proportion of apples people purchase is the same for each season, using a significance level of 0.025. He analyzes the apple purchases each season for a year and records his findings in the following table. Season # of apples purchased ‒‒‒‒‒‒‒‒‒‒‒‒‒‒ (a) In performing this statistical test, state the hypotheses. O Ho: the distribution of apples people purchased is not the same for each season vs. Ha: the distribution of apples people purchased is the same for each season O Ho: the distribution of apples people purchased is the same for each season vs. Ha: the distribution of apples people purchased is not the same for each season O Ho: the observed number of apples people purchased is the same for each season vs. Ha: the observed number of apples people purchased is not the same for each season O Ho: the total number of apples people purchased is not the same for each season vs. Ha: the total number of apples people purchased is the same for each season O Ho: the proportion of customers is the same each season vs. Ha: the proportion of customers is not the same each season (b) What is the expected number of apples purchased for each season? Fill out the table. (Round your answers to 2 decimal places, if needed.) ....... *‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒‒ Fall Spring Summer (c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS= (d) The test statistic follows a chi-square distribution with df = 4 Spring 914 (e) Using the statistical table, the p-value is 0.005

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Mitchell works in the produce section at a small local supermarket and would like to test whether the proportion of apples people purchase is the same for each season, using a significance level of 0.025. He analyzes the apple purchases each season for a year and records his findings in the following table. Season # of apples purchased (a) In performing this statistical test, state the hypotheses. O Ho: the distribution of apples people purchased is not the same for each season vs. Ha: the distribution of apples people purchased is the same for each season O Ho: the distribution of apples people purchased is the same for each season vs. Ha: the distribution of apples people purchased is not the same for each season Ho: the observed number of apples people purchased is the same for each season vs. Ha: the observed number of apples people purchased is not the same for each seas O Ho: the total number of apples people purchased is not the same for each season vs. Ha: the total number of apples people purchased is the same for each season Ho: the proportion of customers is the same each season vs. Ha: the proportion of customers is not the same each season (b) What is the expected number of apples purchased for each season? Fill out the table. (Round your answers to 2 decimal places, if needed.) ******** Fall ‒‒‒‒‒‒‒‒‒‒ Spring ‒‒‒‒‒‒‒‒‒‒ Summer (c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS= (d) The test statistic follows a chi-square distribution with df = 4 + Check (e) Using the statistical table, the p-value is 0.005< p-value < 0.01 + Spring 914 (f) Based on the p-value, those conducting the test should fail to reject the null hypothesis at the significance level of 0.025. (g) What is the appropriate conclusion? There is insufficient evidence to conclude the distribution of apples purchased is not the same for each season. O There is insufficient evidence to conclude the total number of customers for each season are not all the same. There is sufficient evidence to conclude the distribution of apples purchased is not the same for each season. O There is sufficient evidence to conclude the distribution of customers apples purchased is the same for each season. There is sufficient evidence to conclude the total number of customers for each season are not all the same. Summer ******* 877 Winter Fall 914 Winter …….……….. 951 Total 3656
Transcribed Image Text:Mitchell works in the produce section at a small local supermarket and would like to test whether the proportion of apples people purchase is the same for each season, using a significance level of 0.025. He analyzes the apple purchases each season for a year and records his findings in the following table. Season # of apples purchased (a) In performing this statistical test, state the hypotheses. O Ho: the distribution of apples people purchased is not the same for each season vs. Ha: the distribution of apples people purchased is the same for each season O Ho: the distribution of apples people purchased is the same for each season vs. Ha: the distribution of apples people purchased is not the same for each season Ho: the observed number of apples people purchased is the same for each season vs. Ha: the observed number of apples people purchased is not the same for each seas O Ho: the total number of apples people purchased is not the same for each season vs. Ha: the total number of apples people purchased is the same for each season Ho: the proportion of customers is the same each season vs. Ha: the proportion of customers is not the same each season (b) What is the expected number of apples purchased for each season? Fill out the table. (Round your answers to 2 decimal places, if needed.) ******** Fall ‒‒‒‒‒‒‒‒‒‒ Spring ‒‒‒‒‒‒‒‒‒‒ Summer (c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS= (d) The test statistic follows a chi-square distribution with df = 4 + Check (e) Using the statistical table, the p-value is 0.005< p-value < 0.01 + Spring 914 (f) Based on the p-value, those conducting the test should fail to reject the null hypothesis at the significance level of 0.025. (g) What is the appropriate conclusion? There is insufficient evidence to conclude the distribution of apples purchased is not the same for each season. O There is insufficient evidence to conclude the total number of customers for each season are not all the same. There is sufficient evidence to conclude the distribution of apples purchased is not the same for each season. O There is sufficient evidence to conclude the distribution of customers apples purchased is the same for each season. There is sufficient evidence to conclude the total number of customers for each season are not all the same. Summer ******* 877 Winter Fall 914 Winter …….……….. 951 Total 3656
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