Question

1) A random sample of 150 deaths in a given village, the average age of the sample was 70.5 years and the SD was 8 years. Does this show that the average age in this village is greater

than 75 years? Use a significant level of 0.05 .

Answer 1

As we are testing here whether the mean is more than 75 years, therefore the null and the atlernative hypothesis here are obtained as:

The test statistic here is computed as:

For n - 1 = 149 degrees of freedom, as the test statistic value magnitude here is very high, the p-value here that is computed as:
p = P( t₁₄₉ < -6.89) = 0

As the p-value here is approximately 0 < 0.05 which is the level of significance here, therefore the test is significant here and we can therefore reject the null hypothesis here. Therefore we have sufficient evidence here that the average age in this village is greater than 75 years