What is the p-value for this sample? (Report answer accurate to four decimal places.) You wish to test the following claim (Ha) at a significance level of a0.005.Н.: и — 81.5На : д + 81.5You believe the population is normally distributed, but you do not know the standard deviation. You obtain asample of size n =107 with mean M79.2 and a standard deviation of SD = 12.1.What is the test statistic for this sample? (Report answer accurate to three decimal places.)

Answered: You wish to test the following claim…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

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ISBN:9780079039897

Author:Carter

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Chapter10: Statistics

Section10.4: Distributions Of Data

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What is the p-value for this sample? (Report answer accurate to four decimal places.)

You wish to test the following claim (Ha) at a significance level of a
0.005.
Н.: и — 81.5
На : д + 81.5
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a
sample of size n =
107 with mean M
79.2 and a standard deviation of SD = 12.1.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)

Expert Solution

Step 1

As the population standard deviation is not known, we will use t-test.

The provided sample mean is M = $X ˉ = 79.2$ and the sample standard deviation is S.D = $s = 12.1$ , and the sample size is $n = 107$ .

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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