b) The test statistic value is: c) Using the Traditional method, the critical value is: Given p = 0.3714 and N= 35 for the high income group.Test the claim that the proportion of children in the high income group that drew the nickel too large is smaller than 50%. Test at the 0.05 significance level.

Answered: b) The test statistic value is: c)…

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

b) The test statistic value is:

c) Using the Traditional method, the critical value is:

Given p = 0.3714 and N= 35 for the high income group.
Test the claim that the proportion of children in the high income group that drew the nickel too large is smaller than 50%. Test at the 0.05 significance level.

Expert Solution

Step 1

In this scenario, It is appropriate to use one proportion Z test.

Hypotheses:

Let p be the proportion of children in the high income group that drew the nickel too large. The aim is to check that the proportion of children in the high income group that drew the nickel too large is smaller than 50%.

The null hypothesis is H₀ : p=0.5

The alternative hypothesis H_a : p <0.5.

The type of test statistic is one proportion Z test.

Calculation steps:

Test statistic:

Here, n =35 and p^ =0.3715. The hypothetical proportion, p₀ is 0.5. The test statistic for hypothesis test for proportion is given by:

$\begin{array}{rcl} z_{c a l c} & = & \frac{\hat{p} - p}{\sqrt{\frac{p_{0} (1 - p_{0})}{n}}} \\ = & \frac{0.3715 - 0.5}{\sqrt{\frac{0.5 (1 - 0.5)}{35}}} \\ = & \frac{- 0.1285}{0.08452} \\ = & - 1.52 \end{array}$

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