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# Computing value of test statistic

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Consider the following hypothesis test:

Ho: u > 20 (( their is a line under this sine >))
Ha: u < 20
A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.
a. Compute the value of the test statistic.
b. What is the p-value?
c. Using a = .05, what is your conclusion?
d. What is the rejection rule using the critical value? What is your conclusion?

And

Consider the following hypothesis test:
Ho: u = 22
Ha: u =22 ( their is a line throw the = sine hare )

A sample of 75 is used and the population standard deviation is 10. Compute the p-value
and state your conclusion for each of the following sample results. Use a = .01.
a. i = 23
b. i = 25.1
c. i = 20.

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## SOLUTION This solution is FREE courtesy of BrainMass!

A) this is one tailed z test, since population standard deviation is known
z (19.4-20)/(2/sqrt(50)) -2.121320344

B)
P 0.016947427

C) since P value is less than 0.05, we reject Ho

D)
Critical z value -1.644853627
Based on the test, we could conclude that the sample mean is less than 20.

Q2
Since population standard deviation is known, we use z test.
Meanwhile, this is a two tailed test.

a)
Z 0.866025404
P value 0.386476231
We fail to reject Ho since P value is larger than 0.01
There is insufficient evidence to conclude that the sample mean is not equal to 22.

b)
z 2.684678752
P value 0.007259955
We reject Ho since P value is less than 0.01
There is sufficient evidence to conclude that the sample mean is different from 22.

c)
z -1.732050808
P 0.083264517
We fail to reject Ho since P value is larger than 0.01
There is insufficient evidence to conclude that the sample mean is different from 22.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

© BrainMass Inc. brainmass.com October 3, 2022, 12:28 am ad1c9bdddf>
https://brainmass.com/statistics/hypothesis-testing/computing-value-test-statistic-539518