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 With is the manufacturer's claim supported?

Step-by-step explanation:

The question is incomplete. The complete question is:

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.

a. Should z test or t test be used?

b. With a = 0.025, is the manufacturer's claim supported?

Solution:

a) The z test should be used because the population standard deviation is given.

b) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ ≥ 60

For the alternative hypothesis,

µ < 60

This is a left tailed test.

The z score would be determined from the normal distribution table. The formula is

z = (x - µ) / (σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 60

x = 59

σ = 7

n = 81

z = (59 - 60) / (7/√81) = - 1.29

Looking at the normal distribution table, the probability corresponding to the z score is 0.098

Since alpha, 0.025 < than the p value, 0.098, then we would fail to reject the null hypothesis. Therefore, At a 2.5% level of significance, we can conclude that the manufacturer's claim is supported.