Question

H0: u >= 20

Ha: u< 20

A sample of 50 provided a sample mean of 19.6. The population standard deviation is 1.4.

a. Compute the value of the test statistic (to 2 decimals).

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

c. Using = .05, can it be concluded that the population mean is less than 20, Yes or no

d. Using = .05, what is the critical value for the test statistic?

e. State the rejection rule: Reject H0 if z is (select, >=, >, <=, <, =, or not = ) the critical value

f. Using = .05, can it be concluded that the population mean is less than 20? Yes or No

Answer 1

a. Compute the value of the test statistic (to 2 decimals).

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

We are given

Xbar = 19.6

µ = 20

σ = 1.4

n = 50

α = 0.05

Z = (19.6 – 20)/[1.4/sqrt(50)]

Z = -0.4/ 0.19799

Z = -2.02031

Test statistic = -2.02

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

P-value = 0.022

(by using z-table)

c. Using = .05, can it be concluded that the population mean is less than 20, Yes or no

Yes, it can be concluded that the population mean is less than 20, because P-value = 0.022 is less than α = 0.05.

d. Using = .05, what is the critical value for the test statistic?

We have

α = 0.05

Test is lower tailed. So, critical value by using z-table is given as below:

Critical value = -1.6449

e. State the rejection rule:

Reject H₀ if z is < the critical value -1.6449

f. Using = .05, can it be concluded that the population mean is less than 20? Yes or No

Answer: Yes

Test statistic Z = -2.02 is less than critical value -1.6449, so we reject the null hypothesis. So, there is sufficient evidence to conclude that the population mean is less than 20.