Question

A sample of 225 American males showed a mean lifetime of 69.8 years, standard deviation of 4.3 years.

Give 99.73% confidence limits for the mean lifetime of American males.

Answer 1

The variable of interest is mean life time of american males.

Here 225 samples of american male is selected and it is given that the mean life time of american males is 69.8 with standard deviation of 4.3 years.

Let X represents the mean life time of american males in years, then the null hypothesis and alternative hypothesis is given by   

Then the confidence interval under the null hypothesis is given by

We have given

For 99.73% confidence limit, the level of significance is (100-99.73)%=0.27%, therefore the critical Value of Z is

Here the critical value is obtained from the standard normal table with two sided hypothesis testing.

Therefore, the confidence interval for the mean life time under the null hypothesis is given by

Therefore, the confidence interval for 99.73% confidence limit is (68.94, 70.66). Therefore for 99.73% confidence limit the mean life time is greater than 68.94 but less than 70.66.