Question

The following questions all pertain to confidence intervals or hypothesis tests (with regard to the parameter μ, with σ known).

a. If the sample size is divided by a factor of 9, then the width of a confidence interval for μ (for any choice of confidence coefficient) will be multiplied by _______ .  

A. 1/9 B. 9 C. 1/3 D. 3

b. If the sample size n is selected so as to make the 95% margin of error roughly equal to one-fourth of the standard deviation σ, then the sample size n must be _______ .

A. 70 B. 62 C. 68 D. 56

c. If the P-value for the test of H0: μ = μh vs. Ha: μ > μh equals .284, then the P-value for the test of H0: μ = μh vs. Ha: μ < μh could equal _______ .

A. .716 B. .858 C. .568 D. .142

Answer 1

We are given , population standard deviation is known so we have to use standard normal distribution to find confidence interval or Hypothesis test.

a)

Formula for width of a confidence interval for μ is,

Let , sample size is divided by a factor of 9

i.e  width of a confidence interval for μ is multiple of 1/3

Option c is correct !

b)

Formula for width of a confidence interval for μ is,

Sample size n is selected so as to make the 95% margin of error roughly equal to one-fourth of the standard deviation σ

i.e

is critical value for given confidence level.

Confidence level = 95%

Significance level = = 1 - 0.95 = 0.05 ,  /2 = 0.025

So critical value is,

{ Using Excel , =NORMSINV(1-0.025) }

Put this value in above equation and solve for n

square both sides.

Option B is correct !

c)

1) If the P-value for the test of H0: μ = μh vs. Ha: μ > μh is 0.284

then P-value for the test of H0: μ = μh vs. Ha: μ < μh is 1-0.284 = 0.716

Option A is correct !