Answered: A study addressed the issue of whether…

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

Use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion.

A study addressed the issue of whether pregnant women can correctly predict the gender of their baby. Among 104 pregnant women, 57 correctly predicted the gender of their baby. If pregnant women have no such ability, there is a 0.327 probability of getting such sample results by chance. What do you conclude?

Expert Solution

Step 1

The following information is provided: The sample size is $N = 104$ , the number of favorable cases is $X = 57$ , and the sample proportion is $\bar p = \frac{X}{N} = \frac{ 57}{ 104} = 0.5481$ , and the significance level is $\alpha = 0.05$

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

$Ho: p = 0.327$

$H a : p = ̸ 0.32 7 (whether pregnant women can correctly predict the gender of their baby not by chance )$

This corresponds to a two-tailed test, for which a z-test for one population proportion needs to be used.

Rejection Region

Based on the information provided, the significance level is $\alpha = 0.05$ , and the critical value for a two-tailed test is $z_c = 1.96$ .

The rejection region for this two-tailed test is $R = {z : ∣ z ∣ > 1.96}$

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