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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 4 5 6 7 8 Before instruction 20 23 19 26 17 21 24 21 18 After instruction 19 14 13 16 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? 3.

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 4 5 6 7 8 Before instruction 20 23 19 26 17 21 24 21 18 After instruction 19 14 13 16 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? 3.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 82E
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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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