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 17 8 9 9 Key: 17 8 = 178 18 0 0 0 0 1 2 3 4 6 6 7 9 19 0 0 0 1 3 4 5 5 6 6 20 0 0 0 1 2 3 Provided the data from the stem-and-leaf plot above answer the following questions. 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)

Answer 1

Answer:-

Page one

weite observations X: 198 19 199 180 180 180 184 186. 186 187.18.9: 190 194 195. 195 196 196 181 182 183 190: 190 191 200 201 222 203 193 200 mean of the point estimate of a is Ž jne - Exi= 5670 189.00 189. • point estimate for the time (4) teaining emale sunness is 189.00 Sx = sample standard deviation E (8-)2 =79002 hal sx = 7.90 Cade b) Sx . 1810 29 (= 0.991 q=1-C= 0.05, treitical tnal, a/2 = tag, 0. 05/2 2.045 ferm t table : 95040 in for ei is xttnite slot) 7.189 I 2.048 x 7.90. 530 f 189 + 2.95 ( 189-2.95 189 + 2095) [ 186.05, 1995) 3 [186. OSL 4 19 14 95 d) say that We are gos ele confident that the population meancus training time of the female runners is lies between the endpoints of confidence interval (186.05) and /1995)

Page two

C: 0.99, i F= 2 (r: 8.4 Yola : 2.saya 2 sample size, no ne. ( 20/2 20/2) ²0² Ezi (2.57672 8.42 (2)? =111.055 A 117 minimum ample mean The Construct teal ole size 99% (I for the time of female runners is 147 population training time

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