Question

A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr. A random sample of 19 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data support the use of a one-sample t test. The relevant hypotheses are H0: μ = 10 versus Ha: μ < 10. (a) If t = −2.5 and α = 0.05 is selected, what conclusion is appropriate? Reject Fail to reject (b) If t = −1.83 and α = 0.01 is selected, what conclusion is appropriate? Reject Fail to reject (c) If t = 0.57, what conclusion is appropriate? Reject Fail to reject

Answer 1

Fail to reject H0 in all three cases

Explanation:

Given that a certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr.

`H_0: \bar x=10\\H_a \bar x >10`

(Right tailed test at 1% sign level)

n = 19

a) t =-2.5 , df = 18

p = 0.01154

p >1% hence Fail to reject H0

b) t = −1.83

p = 0.041931

p >1% Fail to reject H0

c) t = 0.57

p = 0.287>1% Fail to reject H0