91Ó°ÊÓ

For a random sample of $1020$college graduates, 35 were unemployed.

Hypothesis test:

States the null and alternative hypothesis:

Null hypothesis:

${\mathrm{H}}_0:p_1=p_2$

College graduates do not have a lower unemployment rate than high-school graduates.

Alternative hypothesis:

${\mathrm{H}}_0:p_1<p_2$

College graduates have a lower unemployment rate than high-school graduates.

Calculated the test statistic and $P-$value by MINITAB

MINITAB Output

The value of test statistic is$-3.48$and $P$-value is $0.000.$

If $P≤\mathrm{Î\pm }$, then reject the null hypothesis.

Conclusions

Significant level is $\mathrm{Î\pm }=0.01$

Here, the $P$- value is 0 is lesser than the level of significance is

$P(=0.000)<\mathrm{Î\pm }(=0.01)$

Therefore, by the rejection rule, it can be concluded that there is evidence to reject the null hypothesis ( $\left.H_0\right)$at $\mathrm{Î\pm }=0.01$

Therefore, the data provide sufficient evidence to conclude that college graduates have a lower unemployment rate than high-school graduates.

For a random sample of $1020$ college graduates, 35 were unemployed.

Confidence interval:

Compute confidence interval by MINITAB

MINITAB output

The$98\%$ confidence interval is $(-0.0569,-0.0114)$

There is $98\%$ confidence that the difference in unemployment rates of college and high-school graduates lies between $-0.0569$ and $-0.0114.$