A confidence interval for the population meantells us which values ofare plausible (those inside the interval) and which values are not plausible (those outside the interval) at the chosen level of confidence. You can use this idea to carry out a test of any null hypothesis0:=0starting with a confidence interval: reject0if0is outside the interval and fail to reject if0is inside the interval.

The alternative hypothesis is always twosided,:0because the confidence interval extends in both directions from.A95%confidence interval leads to a test at the5%significance level because the interval is wrong5%of the time. In general, confidence levelleads to a test at significance level =1.

A medical director found the LDL cholesterol=124.86for an SRS of72executives. The standard deviation of the LDL of all adults is =40.

Give a90%confidence interval for the mean LDLof all executives in this company, assuming that the standard deviation is the same as for all adults.

90%confidence interval:

The hypothesized value0=130falls inside this confidence interval. Carry out thetest for0:=130against the twosided alternative.

Find the test statistic.Give your answer to two decimal places.

=

-value:

The hypothesized value0=134falls outside this confidence interval. Carry out thetest for0:=134against the twosided alternative.

Find the test statistic.Give your answer to two decimal places.

=

Find the-valuefor thetest. Give your answer to four decimal places.

-value: