Question

A random sample of 17 observations taken from a population that is normally distributed produced a sample mean of 42.4 and a standard deviation of 8. Find the range for the p-value and the critical and observed values of t for each of the following tests of hypotheses using, α=0.01.

Use the t distribution table to find a range for the p-value.

Round your answers for the values of t to three decimal places.

a. H0: μ=46 versus H1: μ<46.

______ < p-value <_________

tcritical	=
tobserved	=

b. H0: μ=46 versus H1: μ≠46.

_________< p-value <_____

tcritical left	=
tcritical right	=
tobserved	=

Answer 1

a. H0: μ=46 versus H1: μ<46.

Degrees of freedom= n-1= 17-1= 16

Level of SIGNIFICANCE= 0.01

t critical= -2.583

t obs= 42.4-46/8/SQRT (17)

t obs= -3.6/8/4.12

t obs= -3.6/1.942

t obs= - 1.854

P value= 0.041

0.01< pvalue<0.05

Since P value GREATER THAN THE LEVEL OF SIGNIFICANCE THEREFORE NOT SIGNIFICANT.

DECISION: DO NOT REJECT NULL HYPOTHESIS H0.

H0: μ=46 versus H1: μ≠46.

t critical left= -2.921

t critical right= 2.921

t obs= -1.854

P value= 0.0823

Since P value Greater than the level of SIGNIFICANCE therefore NOT SIGNIFICANT.

Decision: Do not REJECT NULL HYPOTHESIS H0.