Question

test the claim about the difference between two population means $mu_1$ and $mu_2$ at the level of significance $alpha$. assume the samples are random and independent, and the populations are normally distributed.
claim: $mu_1=mu_2$, $alpha = 0.01$
population parameters: $sigma_1 = 3.5$, $sigma_2 = 1.7$
sample statistics: $overline{x}_1 = 15$, $n_1 = 31$, $overline{x}_2 = 17$, $n_2 = 26$
determine the alternative hypothesis.
$h_a:mu_1
eqmu_2$
determine the standardized test statistic.
$z=-2.81$ (round to two decimal places as needed.)
determine the $p$-value.
$p$-value $=square$ (round to three decimal places as needed.)

Explanation:

Step1: Calculate the P - value

Since the test is two - tailed (because \(H_a:\mu_1
eq\mu_2\)) and \(z=-2.81\).
The P - value for a two - tailed \(z\) - test is \(P = 2\times(1 - P(Z<|z|))\).
First, find \(P(Z < 2.81)\) using the standard normal distribution table. \(P(Z < 2.81)=0.9975\).

Step2: Compute the final P - value

Then \(P=2\times(1 - 0.9975)\)
\(P = 2\times0.0025=0.005\)

Answer:

\(0.005\)