Question

A manufacturer claims that its televisions have an average lifetime of at least five years (60 months) with a population standard deviation of seven months. Eighty-one televisions were selected at random, and the average lifetime was found to be 59 months. With a=0.025, is the manufacturer's claim supported?

a. critical value= -1.96

test value= 1.29

do not reject the claim since the test value falls in the noncritical region.

there is not enough evidence to reject the manufacture's claim that his televisions have an average lifetime of at least 5 years.

b. critical value= -1.96

test value= -1.29

do not reject the claim since the test value falls in the noncritical region

there is not enough evidence to reject the manufacturer's claim that his televisions have an average lifetime of at least 5 years.

c. critical value= -1.645

test value= -1.29

reject the claim since the test value falls in the noncritical region

there is enough evidence to reject the manufacturer's claim that his televisions have an average lifetime of at least 5 years .

d. critical value= -1.645

test value= 1.29

do not reject the claim since the test value falls in the noncritical region.

there is not enough evidence to reject the manufacturer's claim that his televisions have an average lifetime of at least 5 years.

Answer 1

The statistical software output for this problem is:

One sample Z summary hypothesis test:

μ : Mean of population
H0 : μ = 60
HA : μ < 60
Standard deviation = 7

Hypothesis test results:

Mean	n	Sample Mean	Std. Err.	Z-Stat	P-value
μ	81	59	0.77777778	-1.2857143	0.0993

Hence,

critical value= -1.96

test value= -1.29

do not reject the claim since the test value falls in the noncritical region

there is not enough evidence to reject the manufacturer's claim that his televisions have an average lifetime of at least 5 years.

Option B is correct.