Question

Two samples are randomly selected from each population. The sample statistics are given below.

Answer 1

Answer:

Null hypothesis: $\mu_1 \leq \mu_2$

Alternative hypothesis: $\mu_1 > \mu_2$

The statistic is given by:

$t= \frac{\bar X_1 -\bar X_2}{\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}}$

And replacing we got:

$t=\frac{72.86-67.34}{\sqrt{\frac{15.98^2}{150} +\frac{35.67^2}{275}}}=2.194$

And the best option would be:

2.19

Step-by-step explanation:

We have the following info given:

n1 = 150 n2 = 275

$\bar x_1 = 72.86, \bar x_2 = 67.34$

s1 = 15.98 s2 = 35.67

We want to test the following hypothesis:

Null hypothesis: $\mu_1 \leq \mu_2$

Alternative hypothesis: $\mu_1 > \mu_2$

The statistic is given by:

$t= \frac{\bar X_1 -\bar X_2}{\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}}$

And replacing we got:

$t=\frac{72.86-67.34}{\sqrt{\frac{15.98^2}{150} +\frac{35.67^2}{275}}}=2.194$

And the best option would be:

2.19