Question

In a survey of 12 people, it was found that an average of $36 was spent on their child's last birthday gift with a standard deviation of $11. Estimate the mean amount people spend on their child's last birthday gift with 80% confidence using the appropriate critical value to three decimal places. Enter your answer as equations or as numbers rounded to four decimal places.

Answer 1

(27.3692 ; 44.6308)

Explanation:

Mean, xbar = 36

Standard deviation, s = 11

Sample size, n = 12

Tcritical at 0.2, df = 12 - 1 = 11 ; Tcritical = 2.718

Confidence interval :

Xbar ± Margin of error

Margin of Error = Tcritical * s/sqrt(n)

Margin of Error = 2.718 * 11/sqrt(12) = 8.6308

Confidence interval :

Lower boundary : 36 - 8.6308 = 27.3692

Upper boundary : 36 + 8.6308 = 44.6308

(27.3692 ; 44.6308)