Answer:
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.