# Computing value of test statistic

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.

https://brainmass.com/statistics/hypothesis-testing/computing-value-test-statistic-539518

## 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.

https://brainmass.com/statistics/hypothesis-testing/computing-value-test-statistic-539518