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Chapter 7: Q22E (page 403)

In a test of the hypothesis H0:渭=70versusHa:渭>70, a sample of n = 100 observations possessed meanx炉=49.4and standard deviation s = 4.1. Find and interpret the p-value for this test.

Short Answer

Expert verified

The p-value for the test is 0.9279. The p-value indicates the probability of getting the test statistic is more than -1.46 when the claim 渭=50is true.

Step by step solution

01

Given information

The hypothesis test is: H0:渭=50versus Ha:渭>50.

A random sample of size 100 is selected.

The sample mean is x炉=49.4.

The sample standard deviation is s=4.1.

02

Computing the value of the test statistic

The test statistic is:

z=x炉-渭sn=49.4-504.1100=-0.64.110=-0.60.41=-1.46

The test statistic is z = -1.46.

03

 Step 3: Computing the p-value

The p-value for the right-tailed test is:

p=PZ>-1.46=1-PZ猢�-1.46=1-0.0721=0.9279

The z-table is used to obtain the probability of a z-score less than or equal to -1.46.

Therefore, the p-value is 0.9279.

04

Interpretation of the p-value

The p-value indicates the probability of getting the test statistic is more than -1.46 when the claim渭=50 is true.

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