Question

For each of the following situations, calculate the p-value and determine if H₀ is rejected at a 5% significance level with the test statistic, -1.94. All numbers should be reported to four decimal places.

a) Consider a hypothesis test concerning a population mean with σ known and n = 1300. As stated above the test statistic is -1.94.

H₀: μ = 656 H_a: μ < 656

i) What is the p-value?

ii) Will H₀ be rejected in part a)?

iii) Please submit your computer code for a) here.

b) Consider a hypothesis test concerning a population mean with σ unknown and n = 58. The value of the test statistic is the same and is -1.94.

H₀: μ = 262 H_a: μ ≠ 262

i) What is the p-value?

ii) Will H₀ be rejected in part a)?

iii) Please submit your computer code for a) here.

Answer 1

iii) Using R

> round(pnorm(-1.94),4)
[1] 0.0262

Using Excel

=NORM.DIST(-1.94,0,1,1)

0.0262

iii) Using R

> round(2*pt(-abs(-1.94),df=57),4)
[1] 0.0573

Using Excel

A = T.DIST(1.94,57,1)

A =0.9713

p-value = 2*(1-A)

p-value =

0.0573