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

0.149

Step-by-step 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.