Question

Mario the marriage celebrant is interested in investigating the average age at which people who attended university get married. A sample of 55 individuals who attended university and have been married once has been randomly selected and the age at which each person married was recorded. The sample mean age of marriage was calculated as 31 years old. It is known that the population standard deviation of age of marriage for all people is equal to 11 years. It is assumed that this standard deviation will also apply specifically to the age of marriage for people who attended university. Calculate the upper and lower bounds of the 95% confidence interval for the mean age of marriage for people who attended university. Give your answers in years to 2 decimal places.

Answer 1

The upper bound of the 95% confidence interval for the mean age of marriage for people who attended university is 33.91 years.

The lower bound of the 95% confidence interval for the mean age of marriage for people who attended university is 28.09 years.

Explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1 - 0.95)/(2) = 0.025`

Now, we have to find z in the Ztable as such z has a pvalue of
`1 - \alpha`.

That is z with a pvalue of
`1 - 0.025 = 0.975`, so Z = 1.96.

Now, find the margin of error M as such

`M = z(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

`M = 1.96(11)/(√(55)) = 2.91`

The lower end of the interval is the sample mean subtracted by M. So it is 31 - 2.91 = 28.09 years

The upper end of the interval is the sample mean added to M. So it is 31 + 2.91 = 33.91 years.

The upper bound of the 95% confidence interval for the mean age of marriage for people who attended university is 33.91 years.

The lower bound of the 95% confidence interval for the mean age of marriage for people who attended university is 28.09 years.