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Eight schoolchildren, chosen at random from the first year of a large school, were given, without prior warning, a mathematical task, and the time taken (in minutes) by each child to complete the task was recorded. The following day the children were instructed how to perform such tasks efficiently, and a week later they were tested again on a similar task. Once again, the time taken to complete the task was recorded for each child and the results were as follows. Time taken (minutes) Child 1 2 3 5 6 7 8 Before instruction 26 20 17 21 23 24 21 18 After instruction 19 14 13 16 19 18 16 17 (a) Find a 90% confidence interval for the mean time taken by first year children (i) before instruction, and (ii) after instruction, assuming that times are normally distributed. 4)

Eight schoolchildren, chosen at random from the first year of a large school, were given, without prior warning, a mathematical task, and the time taken (in minutes) by each child to complete the task was recorded. The following day the children were instructed how to perform such tasks efficiently, and a week later they were tested again on a similar task. Once again, the time taken to complete the task was recorded for each child and the results were as follows. Time taken (minutes) Child 1 2 3 5 6 7 8 Before instruction 26 20 17 21 23 24 21 18 After instruction 19 14 13 16 19 18 16 17 (a) Find a 90% confidence interval for the mean time taken by first year children (i) before instruction, and (ii) after instruction, assuming that times are normally distributed. 4)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 32PPS
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Eight schoolchildren, chosen at random from the first year of a large school, were given, without prior warning, a mathematical task, and the time taken (in minutes) by each child to complete the task was recorded. The following day the children were instructed how to perform such tasks efficiently, and a week later they were tested again on a similar task. Once again, the time taken to complete the task was recorded for each child and the results were as follows. Time taken (minutes) Child 1 2 3 4 5 6 7 8 Before instruction 26 20 17 21 23 24 21 18 After instruction 19 14 13 16 19 18 16 17 (a) Find a 90% confidence interval for the mean time taken by first year children (i) before instruction, and (ii) after instruction, assuming that times are normally distributed. (b) Find a 90% confidence interval for the mean difference between times before and after instruction, for first year children. (c) Approximately how many children would have been needed in the sample in order to achieve a confidence interval in part (b) whose total width is 2 minutes?
Transcribed Image Text:Eight schoolchildren, chosen at random from the first year of a large school, were given, without prior warning, a mathematical task, and the time taken (in minutes) by each child to complete the task was recorded. The following day the children were instructed how to perform such tasks efficiently, and a week later they were tested again on a similar task. Once again, the time taken to complete the task was recorded for each child and the results were as follows. Time taken (minutes) Child 1 2 3 4 5 6 7 8 Before instruction 26 20 17 21 23 24 21 18 After instruction 19 14 13 16 19 18 16 17 (a) Find a 90% confidence interval for the mean time taken by first year children (i) before instruction, and (ii) after instruction, assuming that times are normally distributed. (b) Find a 90% confidence interval for the mean difference between times before and after instruction, for first year children. (c) Approximately how many children would have been needed in the sample in order to achieve a confidence interval in part (b) whose total width is 2 minutes?
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