Question

1) Consider a test of

H₀ : μ = μ₀

vs.

H₀ : μ < μ₀.

Suppose this test is based on a sample of size 8, that σ² is known, and that the underlying population is normal. If a 5% significance level is desired, what would be the rejection rule for this test?

		Reject H0 if zobs < -1.645
		Reject H0 if tobs < -1.894
		Reject H0 if zobs < -1.960
		Reject H0 if tobs < -2.306

2)

Which of the following statements about conclusions in a hypothesis test is true?

		If the conclusion at the 5% significance level is to fail to reject H0, then the conclusion at the 1% significance level must be to reject H0.
		If the conclusion at the 1% significance level is to reject H0, then the conclusion at the 5% significance level must also be to reject H0.
		If the conclusion at the 5% significance level is to reject H0, then the conclusion at the 1% significance level must also be to reject H0.
		If the conclusion at the 5% significance level is to fail to reject H0, then the conclusion at the 10% significance level must also be to fail to reject H0.

3)

For a hypothesis test of

H₀ : μ = 8

vs.

H₀ : μ > 8,

the sample mean of the data is computed to be 8.24. The population standard deviation is unknown; the sample standard deviation is computed, and its value is 0.29. These sample statistics are based on a sample size of 19. It is assumed that the underlying population is normally distributed. Which of the following would be the distribution of the test statistic in this scenario?

		The t-distribution with 18 degrees of freedom
		The t-distribution with 8 degrees of freedom
		The standard normal distribution
		The t-distribution with 19 degrees of freedom

Answer 1

1) Consider a test of

H0 : μ = μ0 vs. H0 : μ < μ0

Here σ2 is known and α = 0.05

Critical value = Zα = Z0.05 = 1.645

Ans :A. Reject H0 if zobs < -1.645

2)

Which of the following statements about conclusions in a hypothesis test is true?

if p-value < α then we reject H0 otherwise we Fail the reject H0

Ans:- B.  If the conclusion at the 1% significance level is to reject H0, then the conclusion at the 5% significance level must also be to reject H0.

3)

For a hypothesis test of

H0 : μ = 8 vs. H0 : μ > 8

sample mean = 8.24

s = 0.29 --------(sample standard deviation)

n=19

df = n-1 = 18

Ans : - A. The t-distribution with 18 degrees of freedom