Question

Consider the following hypothesis test:

H ₀:   20

H _a:  < 20

A sample of 60 provided a sample mean of 19.5. The population standard deviation is 2.

a. Compute the value of the test statistic (to 2 decimals). If your answer is negative, use minus "-" sign.

b. What is the p-value (to 3 decimals)?

c. Using  = .05, can it be concluded that the population mean is less than 20? SelectYesNoItem 3

d. Using  = .05, what is the critical value for the test statistic (to 3 decimals)? If your answer is negative, use minus "-" sign.

What is the rejection rule using the critical value?

Reject H ₀ if z Select≤≥=Item 5   

e. What is your conclusion?
Reject H ₀ if z is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 7  the critical value.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 20
Alternative Hypothesis: μ < 20

a)
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (19.5 - 20)/(2/sqrt(60))
z = -1.94

b)
P-value Approach
P-value = 0.0262

c)
As P-value < 0.05, reject the null hypothesis.
Yes, can be concluded

d)
Rejection Region
This is left tailed test, for α = 0.05
Critical value of z is -1.645.

e)
Hence reject H0 if z < -1.645