Question

Suppose that a company claims that its batteries last 250 hours on average. It took many large samples, and each time the mean number of hours was outside the 95% confidence interval. Based on this information alone, which of the following is probably not the mean number of hours that the company's batteries last?

A. 240
B. 245
C. 250
D. 235

Answer 1

C. 250

Explanation:

Confidence interval is used to express the degree of uncertainty associated with a sample statistic.

The confidence interval is calculated as,

`=\mu \pm z(\sigma)/(√(n))`

As here the confidence interval is 95%, we shall use
`z=1.96`.

So the confidence interval will be,

`=250\pm 1.96(\sigma)/(\sqrt n)`

And
`(\sigma)/(\sqrt n)\\eq 0`

As it is given that, each time the mean number of hours was outside the 95% confidence interval, it will be either below or above 250.

Therefore, the value can be anything, but not 250.

Answer 2

The correct choice is C, the reason being the Confidence Interval would have been based on the expected population mean of 250 hours. The means of "many large samples" were all outside the 95% Confidence Interval which was based on the expected population mean of 250 hours.