Compute the 95% confidence interval for the difference between two means. Show your computations for the mean and standard deviation. b. The researcher would conclude that learning occurred if the mean of the second assembly times was less than the mean of the first assembly times. Use hypothesis testing to verify the conclusion at α = 0.05 level of significance. Follow the steps in conducting Hypothesis Testing.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A preschool teacher devised a wooden toy assembly project to test learning in 6-year-olds. The time in seconds
to assemble the project was noted, and the toy was disassembled out of the child’s sight. Then the child was given the task to repeat.

CHILD  1 2 3 4 5 6 7 8 9 10
TRIAL 1 100 150 150 110 130 120 118 110 100 90
TRIAL 2 90 130 150 90 105 110 120 100 90 80

Assume the distribution of times to be approximately normal.
a. Compute the 95% confidence interval for the difference between two means. Show your computations for the mean and standard deviation.
b. The researcher would conclude that learning occurred if the mean of the second assembly times was less than the mean of the first assembly times. Use hypothesis testing to verify the conclusion at α = 0.05 level of significance. Follow the steps in conducting Hypothesis Testing.

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