Question

A consumer group claims that the mean acceleration time from 0 to 60 miles per hour for a sedan is "7.9" seconds. A random sample of 33 sedans has a mean acceleration time from 0 to 60 miles per hour of 7.6 seconds. Assume the population standard deviation is 2.3 seconds. Find the standardized test statistic and the corresponding p-value.

Answer 1

Answer with explanation:

Given claim : A consumer group claims that the mean acceleration time from 0 to 60 miles per hour for a sedan is "7.9" seconds.

Let $\mu$ be the population mean.

Then, the null hypothesis and alternative hypothesis will be :-

$H_0:\mu=7.9\\\\ H_a:\mu\neq7.9$, since the alternative hypothesis is two=tailed , so the test is a two-tailed test.

Test statistic for population mean :-

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

Given : $\overline{x}=7.6\ ;\ \sigma=2.3;\ n=33$

Then, we have

$z=\dfrac{7.6-7.9}{\dfrac{2.3}{\sqrt{33}}}\approx-0.749$

Hence, the standardized test statistic= $z=-0.749$

The p-value (two tailed)= $2P(z>|-0.749|)=0.4538572\approx0.4539$