91Ó°ÊÓ

Sample mean = $125.7$

Sample standard deviation = $29.8$

P-value =$0.0101$

The sample mean $\stackrel{-}{x}$= $125.7$

standard deviation $\mathrm{σ}=29.8$

P-value = role="math" localid="1654319413192" $0.0101=1.01\%$

Calculating the null and alternative hypotheses,

$\begin{array}{rl}& H_o:\mathrm{μ}=115\\ & H_a:\mathrm{μ}>115\end{array}$

Hence when the population mean is$115$, there is a $1.01\%$chance of getting a sample mean of $125.7$

Sample mean =$125.7$

Sample standard deviation =$29.8$

P-value =$0.0101=1.01\%$

The p-value = $0.0101$

When $\mathrm{Î\pm }=0.05$

The p-value is less than $\mathrm{Î\pm }=0.005$

The null hypothesis is rejected

When $\mathrm{Î\pm }=0.01$$\mathrm{Î\pm }=0.01$

The p-value is greater than$\mathrm{Î\pm }=0.01$

The null hypothesis is not rejected

Hence there is enough convincing evidence against the null hypothesis when $\mathrm{Î\pm }=0.05$and not enough convincing evidence against the null hypothesis when$\mathrm{Î\pm }=0.01$