Question

The weekly sales at two movie theaters were recorded for a random sample of 25 weeks. A 95 percent confidence interval for the difference in mean weekly sales for the two movie theaters was calculated as ($1,288,$2,586). With all else remaining constant, which of the following would have resulted in a confidence interval narrower than the calculated interval? A sample size less than 25 A sample size less than 25 A A sample size greater than 25 A sample size greater than 25 B An increase to 99 percent confidence An increase to 99 percent confidence C A sample mean greater than $1,937 A sample mean greater than $1,937 D A sample mean less than $1,937

Answer 1

A sample size greater than 25

Explanation:

Margin of error of a confidence interval:

`M = z(\sigma)/(√(n))`

In which z is related to the confidence level(higher confidence level means higher z)
`\sigma` is the standard deviation of the population and n is the size of the sample.

The higher the margin of error, the wider the interval is.

To have a narrower interval:

For a narrower interval, the margin of error has to be diminished. This can be achieved reducing the confidence level, or increasing the sample size.

In this question:

There are no options that say reducing the confidence level, so we should increase the sample size, that is, a sample size greater than 25.