Question

According to a survey, the average age at which American women have their first child is 26. To test if women in Flagstaff have their first child at a lower age than the national average, a researcher decides to do a hypothesis test, at a 10% significance level. He surveys 20 randomly selected women with children in Flagstaff and asks them about the age at which they had their first child. From the data, the sample mean age is 24.5, and the sample standard deviation (s) is 1.7.

H0: μ≤26; Ha: μ>26.
α=0.1 (significance level)
What is the test statistic (t-value) of this one-mean hypothesis test (with σ unknown)?

Answer 1

The test statistic (t-value) for this one-mean hypothesis test is -3.93.

Step-by-step explanation:

The test statistic (t-value) of this one-mean hypothesis test with an unknown standard deviation can be calculated using the formula:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values:

t = (24.5 - 26) / (1.7 / sqrt(20))

t = -1.5 / (1.7 / 4.47)

t = -1.5 / 0.381

t = -3.93

The test statistic (t-value) for this hypothesis test is -3.93.