Question

A producer claims that the useful life of the radios it produces is more than 15 years. When asked to submit evidence of this claim, he obtains the names of 15 clients from his files and asks each one about the life of the radios. From these measurements he calculates an average lifespan of 17 years with a standard deviation of 2 years. If μ x is the actual mean of the useful life of the radios, what assumption is necessary to be able to test the value of the parameter of interest?

Select one:

a. that the sample comes from a non-normal population.

b. that the variances of the population and the sample are equal.

c. that the population of the useful life of the radios follows a normal distribution.

d. all of the above.

Answer 1

Ans. The correct option is (c), i.e., That the population of the useful life of radios follows a normal distribution.

The parameter of interest in here is the mean useful life of radios, and to which the producer claimed that it is to be 15 years. But by taking a sample of 15 , that is by taking the names of 15 clients and than the average lifespan is calculated as 17years with a standard deviation .

So the claim of producer about the population parameter can be tested by the hypothesis testing, and in order to conduct the hypothesis we should have a normally distributed population or we should have the large sample size.

Since we do not have the large sample size so the necessary condition that remains to satisfy is normal distribution of population.

And this claim can be tested using the following hypothesis:

Null hypothesis,

Alternative hypothesis,

And the formula for the test statistic is :  

And after calculating the test statistic and then using the p-value method we can conclude about the claim which we're testing.