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 hours. A random sample of 20 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data supports the use of a one-sample t test. (a) What hypotheses should be tested if the investigators believe a priori that the design specification has been satisfied?

(b) What conclusion is appropriate if the hypotheses of part (a) are tested, t = −2.3, and α = 0.05? [Round your P-value to three decimal places.] State the conclusion in the problem context.

(c) What conclusion is appropriate if the hypotheses of part (a) are tested, t = −1.8, and α = 0.01? [Round your P-value to three decimal places.] State the conclusion in the problem context.

(d) What conclusion is appropriate if the hypotheses of part (a) are tested, t = −3.6, and α = 0.01? (Round your P-value to three decimal places.) State the conclusion in the problem context.

Answer 1

: true average writing lifetime under controlled conditions

(a) Null hypothesis : H_o : true average writing lifetime under controlled conditions 10 hours ; 10

Alternate Hypothesis : H_a : true average writing lifetime under controlled conditions <  10 hours ; < 10

(b)

sample size : n= 20;

Degrees of freedom = n-1 =20-1=19

t = −2.3, and α = 0.05

For left tailed test :

As P-Value i.e. is less than Level of significance i.e (P-value:0.0165 < 0.05:Level of significance); Reject Null Hypothesis

There is sufficient evidence to conclude that the true average writing lifetime under controlled conditions <  10 hours

(c)

sample size : n= 20;

Degrees of freedom = n-1 =20-1=19

t = −1.8, and α = 0.01

For left tailed test :

As P-Value i.e. is greater than Level of significance i.e (P-value:0.0439 > 0.01:Level of significance); Fail to Reject Null Hypothesis
There is not sufficient evidence to conclude that the true average writing lifetime under controlled conditions <  10 hours

(d)

sample size : n= 20;

Degrees of freedom = n-1 =20-1=19

t = −3.6, and α = 0.01

For left tailed test :

As P-Value i.e. is less than Level of significance i.e (P-value:0.001 < 0.01:Level of significance); Reject Null Hypothesis

There is sufficient evidence to conclude that the true average writing lifetime under controlled conditions <  10 hours