Question

The age of the residents in a certain town is Normally distributed with an unknown mean μ and unknown standard deviation σ . The mayor knows that the average age 10 years ago was 35, but she thinks that the average age is now lower. To test this claim, she acquires a random sample of 40 residents which has a sample mean age of 36 years and a sample standard deviation of 6 years.

If the mayor uses technology, which of the following is the P‑value she will use to test her claim?

0.146

0.292

0.149

0.298

Answer 1

0.149

Explanation:

Here the hypothesized mean=35

Null hypothesis:μ=35

Alternative hypothesis:μ>35

It is clearly stated in the problem that the mayor thinks average age is now lower that is hypothesized mean is greater.

we know that n=40,xbar=36 and s=6.

we don't know about population standard deviation and the estimate sample standard deviation is given so, we use t-test statistic.

t=(xbar-μ)/(sd/sqrt(n))=36-35/6/(sqrt(40)) = 1.0541

The p-value is calculated using t-test statistic and the alternative hypothesis. Using excel function T.DIST.RT(1.0541,39) we get p-value=0.149

RT(right tailed) is used because alternative hypothesis is μ>35.

Hence the p-value is 0.149.