Question

A researcher wishes to test the hypothesis that the mean age at first marriage for women in Texas is less than 23.2. In a sample of 69 Texas women, he finds that the average age is 23.5 with a standard deviation of 4.2.

Calculate the test statistic to two decimal places.

I must be using wrong formula FOR these types of problems, please show step by step, Thanks Business Analysis3363 homework

Answer 1

Here population standard deviation is unknown. So, we are going to use one sample t test.

We want to test the hypothesis that the mean age at first marriage for women in Texas is less than 23.2.

1. Null hypothesis: µ = 23.2

Alternative hypothesis: µ < 23.2

2. This is one-sided test.

We have given Population mean µ = 23.2

Sample mean (X) = 23.5

Sample standard deviation (S) = 4.2

Sample size (n) = 69

Test statistics (t) = (X - µ) / (S/ √n)

t = (23.5 - 23.2)/ (4.2/sqrt(69) = 0.593

Test statistics t = 0.59

The test statistics is 0.59