Question

In a certain city, a researcher wishes to determine whether the average age of its citizens is really 61.2 years, as the mayor claims. A sample of 21 residents has an average age of 59.8 years. The standard deviation of the sample is 1.5 years. At a=1%, is the average age of the residents really 61.2 years?

Answer 1

Here we have to test that

n = 21

Here we have not given Population standard deviation so we will use here one sample t test.

Test statistic:

                 (Round to 2 decimal)

Test is two tailed test.

alpha = level of significance = 1% = 0.01

Critical value for alpha = 0.01 and degrees of freedom = n - 1 = 21 - 1 = 20 is

t critical = 2.845                    (From statistical table of t values)

Here |t0| = 4.28 > t critical = 2.845

So we reject null hypothesis H0.

Conclusion: There is insufficient evidence to conclude that the average age of the residents is really 61.2 years.