A researcher was interested in whether men tend to show sign

A researcher was interested in whether men tend to show signs of Alzheimer’s disease at an earlier age than women. She randomly selected two samples of 65 men (N1) and 70 women (N2) to test the hypothesis. The mean age of onset of Alzheimer’s symptoms for men is 68.6 with a standard deviation of S1=6.1, and for the mean age women is 66.5 with a standard deviation of S2=5.2. At 95% level, test the null hypothesis that there is no difference between the age of onset of Alzheimer’s symptoms for men and women.

Solution

H0: Two means are equal

Ha: Two means are not equal

Two tailed test

As only std dev of sample is known use t test

SEM    0.757      0.622

Std error of difference = 0.973

mu1- mu2 = 2.100

df = 133

t statistic = 2.1574

p value = 0.0328

As p < alpha= 0.05 we reject null hypothesis

The two two means have significant differences.