Question

A random sample of 18 size aa batteries for toys yield a mean of 3.74 hours with standard deviation, 0.63 hours. (a) find value of t (the multiplier) that would be used to create a 99% ci. t = (b) find the margin of error for a 99% ci.

Answer 1

a) t = 2.8982

b) 1.826

Explanation:

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 = 18 - 1 = 17

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.99)/(2) = 0.995([tex]t_(.995)`). So we have T = 2.8982. This is the answer for a.

The margin of error is:

M = T*s = 2.8982*0.63 = 1.826

In which s is the standard deviation of the sample.