Question

A researcher wants to assess if there is a difference in the average age of onset of

a type of kidney disease for men and women. Let the population 1 mean be the

average age of onset for women and the population 2 mean be the average age

of onset for men. A random sample of 27 women with the disease showed an

average age of onset to be 81 years, with a sample standard deviation of 13.5

years. A random sample of 22 men with the disease showed an average age

of onset to be 79 years with a sample standard deviation of 6.5 years. Assume

that ages at onset of this disease are normally distributed for each gender also

assume unequal variance. Conduct a hypothesis test at the .05 level of

significance to determine if there is a difference in the onset ages between

men and women. What are the null and alternative hypotheses? What is the value of the test statistic? What is/are the critical value(s)? What is the decision? And What is the conclusion?

Answer 1

Population 1 is for women and Population 2 is for men

Null Hypothesis H0: mu1 = mu2

Alternative Hypothesis H1: mu1 not equal to mu2

Given, n1 = 27, Xbar1 = 81, S1 = 13.5

n2 = 22, Xbar2 = 79, S2 = 6.5

alpha = 0.05

test statistic is

after substituting values

t0 = 0.6792178

degrees of freedom = n1 + n2 - 2 = 27 + 22 - 2 = 47

t_critical at 0.05 significance and df = 47 for two tailed is = 2.011741

Decision: As t_critical > t0, we fail to reject H0

Conclusion: at alpha = 0.05 level of significance we don't have enough evidence to state that there is a difference in the average age of onset of a type of kidney disease for men and women