Question

A report by the Gallup Poll stated that on average a woman visits her physician 5.8 times a year. A researcher randomly selects 20 women and obtained these data. The population standard deviation is 2

3    2    1    3    7     2     9     4     6     6    8   0   5   6   4    2   1   3   4    1

At α= 0.01 can it be concluded that the average is still 5.8 visits per year? Use the traditional method.

Answer 1

Null Hypothesis, Ho: The average number of visits woman makes to her physician is 5.8 times a year i.e.

Alternative Hypothesis, Ha: The average number of visits woman makes to her physician is significantly different from 5.8 times a year i.e.

Test - Statistics: Under Ho,

  

Here, and  

Rejection Region: The critical values of Z at alpha = 0.01 are Zcrit = +-2.58. So Rejection Region is given as:

R = { Z : |Z| > 2.58}

Conclusion: Since, |Z| = 4.3603 > 2.58 so we Reject Ho at 1 % significance and conclude that The average number of visits woman makes to her physician is significantly different from 5.8 times a year i.e.