Question

A random sample has been selected from a population. The point estimate = 78.65 and margin of error E = 8.24 for a 90% confidence level have been calculated for you. Construct the confidence interval that corresponds to this information.

Answer 1

90% confidence interval: (70.41,86.89)

Explanation:

We are given the following in the question:

Point estimate = 78.65

Margin of error, E = 8.24

Confidence level = 90%

Significance level = 10%

Formula:

`\text{Point estimate} \pm \text{Margin of error}`

Putting the values, we get,

`z_(critical)\text{ at}~\alpha_(0.10) = \pm 1.64`

`78.65 \pm 8.24 = (70.41,86.89)`

(70.41,86.89) is the required 90% confidence interval.