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Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others? Owners of a children's toy store chain asked this question. Some data collected by the chain are summarized in the table below. The data were obtained from a random sample of 160 people. The birthdate of each person was recorded, and each of these dates was placed into one of four categories: winter (December 21-March 20), spring (March 21-June 20), summer (June 21-September 20), and fall (September 21-December 20). The numbers in the first row of the table are the frequencies observed in the sample for these season categories. The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year. The bottom row of numbers gives the following value for each of the season categories. (fo-E) JE Part 1 (ObservettequencyExpectefrequency Expectefrequency Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. (0-1) JE Round your Send data to Excel responses to three or more decimal places. ? B Winter Spring Summer Fall Total X Observed frequency fo 31 41 47 41 160 Expected frequency JE D 0 JE 0 40.00 40.00 D 1.225 0.025 Part 2 Answer the following to summarize the test of the hypothesis that birthdays are equally likely during each season of the year. Use the 0.05 level of significance for the test. (a) Determine the type of test statistic to use. X Type of test statistic: (Choose one) (b) Find the value of the test statistic. (Round your answer to two or more decimal places.) (c) Find the p-value. (Round your answer to three or more decimal places.) 0 (d) Can we reject the hypothesis that birthdays are equally likely during each season of the year? Yes No

Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others? Owners of a children's toy store chain asked this question. Some data collected by the chain are summarized in the table below. The data were obtained from a random sample of 160 people. The birthdate of each person was recorded, and each of these dates was placed into one of four categories: winter (December 21-March 20), spring (March 21-June 20), summer (June 21-September 20), and fall (September 21-December 20). The numbers in the first row of the table are the frequencies observed in the sample for these season categories. The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year. The bottom row of numbers gives the following value for each of the season categories. (fo-E) JE Part 1 (ObservettequencyExpectefrequency Expectefrequency Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. (0-1) JE Round your Send data to Excel responses to three or more decimal places. ? B Winter Spring Summer Fall Total X Observed frequency fo 31 41 47 41 160 Expected frequency JE D 0 JE 0 40.00 40.00 D 1.225 0.025 Part 2 Answer the following to summarize the test of the hypothesis that birthdays are equally likely during each season of the year. Use the 0.05 level of significance for the test. (a) Determine the type of test statistic to use. X Type of test statistic: (Choose one) (b) Find the value of the test statistic. (Round your answer to two or more decimal places.) (c) Find the p-value. (Round your answer to three or more decimal places.) 0 (d) Can we reject the hypothesis that birthdays are equally likely during each season of the year? Yes No

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
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others? Owners of a children's toy store chain asked this question. Some data collected by the chain are summarized in the table below. The data were obtained from a random sample of 160 people. The birthdate of each person was recorded, and each of these dates was placed into one of four categories: winter (December 21-March 20), spring (March 21-June 20), summer (June 21-September 20), and fall (September 21-December 20). The numbers in the first row of the table are the frequencies observed in the sample for these season categories. The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year. The bottom row of numbers gives the following value for each of the season categories. (fo-E) JE Part 1 (ObservettequencyExpectefrequency Expectefrequency Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. (0-1) JE Round your Send data to Excel responses to three or more decimal places. ? B Winter Spring Summer Fall Total X Observed frequency fo 31 41 47 41 160 Expected frequency JE D 0 JE 0 40.00 40.00 D 1.225 0.025 Part 2 Answer the following to summarize the test of the hypothesis that birthdays are equally likely during each season of the year. Use the 0.05 level of significance for the test. (a) Determine the type of test statistic to use. X Type of test statistic: (Choose one) (b) Find the value of the test statistic. (Round your answer to two or more decimal places.) (c) Find the p-value. (Round your answer to three or more decimal places.) 0 (d) Can we reject the hypothesis that birthdays are equally likely during each season of the year? Yes No
Transcribed Image Text:Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others? Owners of a children's toy store chain asked this question. Some data collected by the chain are summarized in the table below. The data were obtained from a random sample of 160 people. The birthdate of each person was recorded, and each of these dates was placed into one of four categories: winter (December 21-March 20), spring (March 21-June 20), summer (June 21-September 20), and fall (September 21-December 20). The numbers in the first row of the table are the frequencies observed in the sample for these season categories. The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year. The bottom row of numbers gives the following value for each of the season categories. (fo-E) JE Part 1 (ObservettequencyExpectefrequency Expectefrequency Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. (0-1) JE Round your Send data to Excel responses to three or more decimal places. ? B Winter Spring Summer Fall Total X Observed frequency fo 31 41 47 41 160 Expected frequency JE D 0 JE 0 40.00 40.00 D 1.225 0.025 Part 2 Answer the following to summarize the test of the hypothesis that birthdays are equally likely during each season of the year. Use the 0.05 level of significance for the test. (a) Determine the type of test statistic to use. X Type of test statistic: (Choose one) (b) Find the value of the test statistic. (Round your answer to two or more decimal places.) (c) Find the p-value. (Round your answer to three or more decimal places.) 0 (d) Can we reject the hypothesis that birthdays are equally likely during each season of the year? Yes No
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