Question

Consider the following hypothesis test:

H ₀: 20

H _a: < 20

A sample of 55 provided a sample mean of 19.5. The population standard deviation is 1.8.

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? SelectYesNo

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≤≥=

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

Answer 1

Given that, population standard deviation = 1.8

sample size (n) = 55 and sample mean = 19.5

The null and alternative hypotheses are,

H0 : μ = 20

Ha : μ < 20

a) Test statistic is,

=> Test statistic is, Z = -2.06

b) p-value = P(Z < -2.06) = 0.0197

=> p-value = 0.0197

c) Since, p-value = 0.0197 < 0.05, we reject H0 and conclude that the population mean is less than 20.

Answer : Yes

d) critical value at significance level of 0.05 is, Z_{​​​​​​crit} = -1.645

Rejection Rule : Reject H0 if z ≤ -1.645

e) Since, z = -2.06 ≤ -1.645, we should reject HO.