You wish to test the following claim (Ha) at a significance level of a = 0.005. H.:µ = 81.5 Ha:µ + 81.5 You believe the population is normally distributed, but you do not know the standard deviation sample of sizen = 107 with mean M = 79.2 and a standard deviation of SD = 12.1.
You wish to test the following claim (Ha) at a significance level of a = 0.005. H.:µ = 81.5 Ha:µ + 81.5 You believe the population is normally distributed, but you do not know the standard deviation sample of sizen = 107 with mean M = 79.2 and a standard deviation of SD = 12.1.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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Step 1
As the population standard deviation is not known, we will use t-test.
The provided sample mean is M = and the sample standard deviation is S.D = , and the sample size is .
The following null and alternative hypotheses need to be tested:
Ho: μ = 81.5
Ha:μ ≠ 81.5
This corresponds to a two-tailed test.
The t-statistic is computed as follows:
The p-value with 106 degrees of freedom and for t=-1.966 for the two-tailed test is 0.0519(from t-distribution table).
As the p-value is greater than the significance level, i.e.,0.0519≥0.005, the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population meanμ is different than 81.5, at the 0.005 significance level.
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