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

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

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 \\eq 23.5\text{ years}`

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

Formula:

`t_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }`

Putting all the values, we have

`t_(stat) = \displaystyle(24.3 - 23.5)/((5.3)/(√(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.