Question

In the children’s game Don’t Break the Ice, small plastic ice cubes are squeezed into a square frame. Each child takes a turn tapping out a cube of "ice" with a plastic hammer, hoping that the remaining cubes don’t collapse. For the game to work the cubes must be big enough so that they hold each other in place but not so big that they are too difficult to tap out. In an SRS of 43 "ice cubes" the average width was 29.5 millimeters with a standard deviation of 0.12mm. Construct a 95% confidence level for the true mean width. Group of answer choices

Answer 1

(29.46 mm, 29.54 mm).

Explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 43 - 1 = 42

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 42 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.95)/(2) = 0.975`. So we have T = 2.018

The margin of error is:

`M = T(s)/(√(n)) = 2.018(0.12)/(√(43)) = 0.04`

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 29.5 mm - 0.04mm = 29.46 mm

The upper end of the interval is the sample mean added to M. So it is 29.5 mm + 0.04mm = 29.54 mm

The 95% confidence level for the true mean width is: (29.46 mm, 29.54 mm).