Question

Consider the following hypothesis test.

H₀: μ ≥ 35

H_a: μ < 35

A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use

α = 0.01.

A.

x = 34 and s = 5.2

Find the value of the test statistic. (Round your answer to three decimal places.)

B.
Find the p-value. (Round your answer to four decimal places.)

C.

x = 33 and s = 4.5

Find the value of the test statistic. (Round your answer to three decimal places.)

D.

Find the p-value. (Round your answer to four decimal places.)

E.

x = 36 and s = 5.0

Find the value of the test statistic.

F

Find the p-value. (Round your answer to four decimal places.)

Answer 1

A)

Test statistics

t = ( - ) / ( S / sqrt(n) )

= ( 34 - 35) / ( 5.2 / sqrt(36) )

= -1.154

B)

Form T table, With df = 35

P(t < -1.154) = 0.1282

C)

Test statistics

t = ( - ) / ( S / sqrt(n) )

= ( 33 - 35) / ( 4.5 / sqrt(36) )

= -2.667

d)

Form T table, With df = 35

P(t < -2.667 ) = 0.0058

E)

Test statistics

t = ( - ) / ( S / sqrt(n) )

= ( 36 - 35) / ( 5 / sqrt(36) )

= 1.2

F)

Form T table, With df = 35

P(t > 1.2 ) = 0.8809