Q.38 - The Practice of Statistics for AP

Question

For Yvonne's survey, 96 students in the sample said they seldom or never argue with friends.

(a) Calculate the test statistic.

(b) Find the P-value using Table A. Show this result as an area under a standard Normal curve.

Step-by-Step Solution

Answer

a. The test statistic is$-2.18$

b. The P-value is$0.0101$

Step 1: Introduction

A p-value is a factual estimation used to approve a theory against noticed information. A p-esteem estimates the likelihood of getting the noticed outcomes, it is consistent with expectations that the invalid speculation. The lower the p-esteem, the more prominent the factual meaning of the noticed distinction.

Step 2: Explanation Part (a)

The population proportion is p = $0.72$

Number of trials is n = $150$

Number of success is p = $96$

Using,

$z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}$

$=\frac{0.64-0.72}{\sqrt{\frac{0.72(1-0.72)}{150}}}=-2.18$

 Hence the test statistic value is $-2.18$

Step 3: Explanation Part (b)

Calculating the p-value,

$=2\times P\left(\right|Z|>-2.18)$

$=0.0292$

The graph is shown,