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)…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 6E: List the sample space of each experiment. Tossing three coins

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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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