Question

A researcher claims that the mean age of the residents of a small town is more than 32 years. The ages (in years) of a random sample of 36 residents are listed below. At α=0.10, α = 0.10 , alpha equals , 0.10 , comma is there enough evidence to support the researcher's claim? Assume the population standard deviation is 9 years. 41,33,47,31,26,39,19,25,23,31,39,36,41,28,33,41,44,40,30,29,46,42,53,21,29,43,46,39,35,33,42,35,43,35,24,21

Answer 1

From the given data, mean of the sample = 35.083 years. Since population standard deviation is given, we use the same to calculate the test statistic.

= 32 years, = 35.083 years, = 9 years, n = 36, = 0.10

The Hypothesis:

H0: = 32

Ha: > 32

This is a right tailed Test.

The Test Statistic: The test statistic is given by the equation:

The p Value:    The p value (Right Tail) for Z = 2.06, is; p value = 0.0197

The Critical Value:   The critical value (Right Tail) at = 0.10, Zcritical = +1.282

The Decision Rule: If Zobserved is > Zcritical, then Reject H0

Also if P value is < , Then Reject H0.

The Decision:   Since Zobserved (2.06) is > Zcritical (1.282), We Reject H0.

Also since P value (0.0197) is < (0.10) , We Reject H0.

The Conclusion: There is sufficient evidence at the 90% significance level to support the claim that the mean age of the residents of a small town is more than 32 years.