Question

In 1960, census results indicated that the age at which men in a certain region first married had a mean of 23.5 years. We want to find out if the mean age of first marriage has changed/differed from 23.5 years (µ≠23.5) since then. The 40 men in our sample first married at an average age of 24.3 years, with a sample standard deviation s of 5.3 years. The P-value is 0.346. State the conclusion using α = 0.10.

Answer 1

Answer:

There is not sufficient evidence that the mean age of first marriage differs the mean age in 1960.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 23.5 years

Sample mean, $\bar{x}$ = 24.3 years

Sample size, n = 40

Alpha, α = 0.10

Sample standard deviation, s = 5.3 years

P-value = 0.346

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 23.5\text{ years}\\H_A: \mu \neq 23.5\text{ years}$

We use Two-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{24.3 - 23.5}{\frac{5.3}{\sqrt{40}} } = 0.9546$

P-value = 0.346

Since the calculated p-value is greater than the significance level, we fail to reject the null hypothesis and accept the null hypothesis.

Conclusion:

Thus, there is not sufficient evidence that the mean age of first marriage differs the mean age in 1960.