A random sample of 10 single mothers was drawn from a Obstetrics Clinic. Their ages are 22, 17, 27, 20, 23, 19, 24, 18, 19, and 24 years. Test to determine if we can infer at the 5% significance level that the population mean is not equal to 20.

The two-tailed P value equals 0.2308

By conventional criteria, this difference is considered to be not statistically significant.

Step-by-step explanation:

Given is a random sample of 10 single mothers

the ages are given as

22, 17, 27, 20, 23, 19, 24, 18, 19, and 24 years

H0: Mean = 20

Ha: Mean not equals 20

(two tailed test at 5% significance level)

The hypothetical mean is 20.00

The actual mean is 21.30

The difference between these two values is 1.30

The 95% confidence interval of this difference:

From - 0.99 to 3.59

t = 1.2851

df = 9

standard error = 1.012

The two-tailed P value equals 0.2308

By conventional criteria, this difference is considered to be not statistically significant.