Question

(3 pt.) 5. Listed below are the ages of randomly selected race car drivers. of randomly selected race car drivers. Construct a 98% confidence interval estimate of the mean age of all race car drivers. Assur the mean age of all race car drivers. Assume that this data is normally distributed. 32 32 33 33 41 29 38 32 33 23 27 45 52 29 25

Answer 1

X 32 X - mean -1.6 32 -1.6 -0.6 33 33 41 -0.6 7.4 -4.6 4.4 29 38 (X-mean) 2 2.56 2.56 0.36 0.36 54.76 21.16 19.36 2.56 0.36 112.36 43.56 129.96 338.56 21.16 73.96 -1.6 32 33 23 -0.6 -10.6 -6.6 11.4 18.4 -4.6 -8.6 52 25

Since we know that

Mean() - Σ1 ;

Where n is the number of data points
Now

Στη = 504.0 1-1

and n = 15
This implies that

504.0 Mean(T) = 15 Mean(T) = 33.6

Since we know that

Variance(82) – Eti – 7)? -1 n Sri – 7)2 = 823.6 n = 15 Variance(52) - 823.6 Variance(s?) = 58.8286 Standard Deviation(s) = V Variance Standard Deviation(s) = 7.67

Mean ($\bar{x}$) = 33.6
Sample size (n) = 15
Standard deviation (s) = 7.67
Confidence interval(in %) = 98

ta/2.n-1 = 2.624

Since we know that

Confidence interval = ī ta/2,1–17

Required confidence interval =
(33.6 – 2.624.07, 33.6 +2.6247.07 V15' V15

Required confidence interval = (33.6-5.1965, 33.6+5.1965)
Required confidence interval = (28.4035, 38.7965)
Please hit thumps up if the answer helped you.