Question 1196778: Question # 8: Review Part 2: Hypothesis Testing: Find test statistic and p-value and make conclusion for a mean (using T-Test).
x= 137
s = 14.2
n = 20
Ho: μ = 132
H subscript A colon space mu not equal to 132
α = 0.1
Test statistic: t = 1.57
p-value = 0.1318
Reject Ho in favor of HA
There is enough evidence to show that the mean is significantly different from 132.
Test statistic: t = 1.57
p-value = 0.1318
Fail to reject Ho
There is not enough evidence to show that the mean is significantly different from 132.
Test statistic: t = 1.57
p-value = 0.0582
Reject Ho in favor of HA
There is enough evidence to show that the mean is significantly different from 132.
Test statistic: t = 1.57
p-value = 0.0582
Fail to reject Ho
There is not enough evidence to show that the mean is significantly different from 132.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Given info:
xbar = 137
s = 14.2
n = 20
alpha = 0.1
Null Hypothesis: mu = 132
Alternative Hypothesis: mu =/= 132
This is a two-tailed test because of the "not equal" sign in the alternative hypothesis.
Test Statistic:
t = (xbar - mu)/(s/sqrt(n))
t = (137 - 132)/(14.2/sqrt(20))
t = 1.57469575880267
t = 1.57
Use technology to compute the p-value. There are many methods that it would take a while to go over them all, but here's one free online calculator you can use
https://www.statology.org/t-score-p-value-calculator/
Type in 1.57 as the t score and 19 as the degrees of freedom (since df = n-1 = 20-1 = 19)
We're doing a two-tailed test.
Don't worry about the significance level since all we care about is the p-value.
You should get a p-value of roughly 0.1329 from this two-tailed test.
I'm curious to know where your teacher is getting 0.1318 from, but this might be from a reference table of some sort.
Rule: if p-value is smaller than alpha, then reject the null.
Since the p-value is not smaller than alpha, this means we fail to reject the null.
There isn't enough evidence to overturn it.
We don't have enough evidence to show the mean is significantly different from 132.
So for now we conclude that mu = 132 is the case.
Answer: Choice B
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