mixture is normally distributed with $=69.$ Let $$ denote the true average compressive strength.

$($a$)$ What are the appropriate null and alternative hypotheses?

The test statistic has an exponential distribution.

The test statistic has a normal distribution.

The test statistic has a gamma distribution.

The test statistic has a binomial distribution.

If $\stackrel{}{x}=1,340,$ find the $P-$value. $($Round your answer to four decimal places.$)$

$P-$value $=$

Should $H_0$ be rejected using a significance level of $0\mathrm{.}01?$

reject $H_0$

do not reject $H_0$

$($c$)$ What is the probability distribution of the test statistic when $=1,350$ and $n=15?$

The test statistic has an exponential distribution.

The test statistic has a normal distribution.

$$ The test statistic has a binomial distribution.

The test statistic has a gamma distribution.

State the mean and standard deviation $($in $K\frac{N}{m^2})$ of the test statistic. $($Round your standard deviation to three decimal places.$)$

me

$1350,K\frac{N}{m^2}$

standard deviation

$b$