Question

Hi, can you help me answer this question please, thank you

Answer 1

The sample taken was n=66 companies

The sample mean obtained is 7.5 years

The sample standard deviation obtained was 5.3 years

You have to work with a significance level of α= 0.05

And test the statistic hypotheses:

`\begin{gathered} H_0\colon\mu\ge8 \\ H_1\colon\mu<8 \end{gathered}`

a) The test statistic to use, considering that we can assume a normal distribution and the sample size is greater than n=30, is the standard normal

`Z=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt[]{n}}}`

You can calculate the statistic under the null hypothesis as follows:

`\begin{gathered} Z_(H0)=\frac{7.5-8}{\frac{5.3}{\sqrt[]{66}}} \\ Z_(H0)=-0.7664\approx-0.766 \end{gathered}`

b) The p-value is the probability corresponding to the calculated statistic if possible under the null hypothesis.

This test is one-tailed to the left, so the p-value is the accumulated probability to the statistic:

`p-value=P(Z\leq-0.766)=0.2218`

c) The p-value is greater than α, so the decision is to not reject the null hypothesis.