Question

1. Which of the following statements is true?

	a	If a hypothesis test is conducted at the 5% significance level, then a p-value of 0.087 would lead the researcher to reject H0.
	b	A 99% z-based confidence interval of the population mean μ based on a sample will be narrower than a 95% z-based confidence interval of the population mean μ based on the same sample.
	c	When division by a factor of n-1 is used, the sample variance s2 is an unbiased estimator of the population variance σ2.
	d	The t-distribution with 1 degree of freedom is equivalent to the standard normal distribution.

8. 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?

	a	Reject H0 if zobs < -1.645
	b	Reject H0 if tobs < -1.894
	c	Reject H0 if tobs < -2.306
	d	Reject H0 if zobs < -1.960

9. For a test of

H₀ : μ = μ₀

vs.

H₁ : μ > μ₀,

assume that the test statistic follows a t-distribution with 19 degrees of freedom. What is the critical value of the test if a 5% significance level is desired? (Express your answer as a positive decimal rounded to three decimal places.)

10. For a particular scenario, we wish to test the hypothesis H₀ : μ = 13.1. For a sample of size 46, the sample mean X̄ is 11.2. The population standard deviation σ is known to be 8.3. Compute the value of the test statistic z_obs. (Express your answer as a decimal rounded to two decimal places.)

Answer 1

Solution:

1)

Correct option is

When division by a factor of n-1 is used, the sample variance s² is an unbiased estimator of the population variance σ².

8)

Left tailed test

Critical value is =

Reject H₀ if z_obs < -1.645

9)

df = 19

= 5% = 0.05

Observe the alternative hypothesis H₁ : μ > μ₀,

> sign indicates Right tailed test

Critical value is t_0.05,19 = 1.729

Answer: 1.729

10)

The test statistic z is given by

z =

= (11.2 - 13.1) / (8.3/46)

= -1.55