Question

Seventeen of the most recent tweets by @A_single_bear have a mean of 174.88 retweets and a sample standard deviation of 81.64 retweets. Assuming that the distribution of the number of retweets is normal, construct a 90% confidence interval for the mean number of retweets this account gets.

Answer 1

Solution :

t_{$\alpha$ /2,df} = 1.746

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 1.746 * (81.64 / $\sqrt$ 17)

Margin of error = E = 34.57

The 90% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

174.88 - 34.57 < $\mu$ < 174.88 + 34.57

140.31 < $\mu$ < 208.45

(140.31 , 208.45)