Question

The stem-and-leaf plot below shows the marathon training times (in minutes) for a random sample of 30 female runners. Training Times (in minutes) of Female Runners 8 99 Key: 17 8 = 178 18 0 0 0 0 1 2 3 4 6 6 7 9 19 0 0 0 3 4 5 5 6 6 20 0 0 1 2 3 Provided the data from the stem-and-leaf plot above answer the following questions. 1 a) Use the sample to find a point estimate (round to 2 DP) for the mean training time of the female runners. b) Find the sample standard deviation (round to 2 DP) of the training time for the female runners. c) Use the sample to construct a 95% confidence interval for the population mean training time of the female runners. d) Interpret the result of Exercise 3. Write your answer in a complete sentence (Capitalization, Punctuation, etc) e) A trainer wants to estimate the population mean training time for female runners within 2 minutes. Determine the minimum sample size required to construct a 99% confidence interval for the population mean training time of female runners. Assume the population standard deviation is 8.4 minutes. Write your answer in a complete sentence (Capitalization. Punctuation, etc) A/

Answer 1

(a) 189.00

(b) 7.90

(c) (186.05, 191.95)

(d) We are 95% confident that the true population mean training time of the female runners is between 186.05 and 191.95.

(e) n = (2.576*8.4/1)^2 = 469

mean	189.00
sample standard deviation	7.90
confidence interval 95.% lower	186.05
confidence interval 95.% upper	191.95
margin of error	2.95
t(df = 29)	2.045