Answered: doctor used to believe that babies were…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A doctor used to believe that babies were equally likely to be born any day of the week, but with the rise in scheduled deliveries, the doctor now claims that babies are twice as likely to be born on a weekday (Monday through Friday) than on a weekend (Saturday and Sunday). She decides to test:

H_a: Not all of the p_i’s are as stated.

She selects a random sample of 120 babies born this year and determines on which day of the week they were born. She finds that 4 were born on Sunday, 24 on Monday, 21 on Tuesday, 18 on Wednesday, 22 on Thursday, 28 on Friday, and 3 on Saturday. The chi-square test statistic for goodness of fit is χ² = 12.95 and the P-value is between 0.025 and 0.05.

The doctor had hypothesized that babies are twice as likely to be born on a weekday (Monday through Friday) than on a weekend (Saturday and Sunday). Because the P-value is less than 0.05 the doctor rejects the null hypothesis. She completes a follow-up analysis. Here is a table of the observed counts, the expected counts, and the components of the chi-square test statistic:

Based upon the follow-up analysis, why was the null hypothesis rejected?

Although births are less likely on the weekends, births are more than twice as likely during the week.

Although births are less likely on the weekdays, births are more than twice as likely during the weekend.

The doctor was off track. She should have hypothesized that births are equally likely for all days of the week.

The doctor was off track. She should have hypothesized that babies are twice as likely to be born on a weekend (Saturday and Sunday) than on a weekday (Monday through Friday).

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