A random sample of 40 adults with no children under the age of 18 years results

Question

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.76 hours, with a standard deviation of 2.39 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.28 hours, with a standard deviation of 1.62 hours. Construct and interpret a 95% confidence interval for the mean difference in leisure time between adults with no children and adults with children mu_1 - mu_2) Let mu_1 represent the mean leisure hours of adults with no children under the age of 18 and mu_2 represent the mean leisure hours of adults with children under the age of 18. The 95% confidence interval for mu_1, - mu_2) is the range from hours to hours. (Round to two decimal places as needed.) What is the interpretation of this confidence interval? A. There is 95% confidence that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours. B. There is a 95% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours. C. There is a 95% probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours. D. There is 95% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours.

Explanation / Answer

Hence, the interval is[ (5.76 - 4.28) +- 1.96 /sqrt(40) * sqrt( 1.62^2+2.39^2) =( 1.48 - 0.8947, 1.48+0.8947) = (0.5853,2.3747)

P-value for the sample is 0.002 which is significant at alpha of 0.05

Hence, the correct answer is C. There is a 95% probability that difference of means is in the interval and there is enough evidence to neglect the null hypothesis and conclude that there is significant difference.

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