Question

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.16 hours, with a standard deviation of 2.42 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.16 hours, with a standard deviation of 1.58 hours. Construct and interpret a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children (141 - H2). Let Hy represent the mean leisure hours of adults with no children under the age of 18 and 12 represent the mean leisure hours of adults with children under the age of 18. hours to hours. The 90% confidence interval for (H1 - H2) is the range from (Round to two decimal places as needed.) What is the interpretation of this confidence interval? O A. There is a 90% 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. OB. There is 90% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours. O C. There is 90% 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. OD. There is a 90% probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours.

Answer 1

i am using minitab to solve the problem.

steps:-

copy the data in minitab $1596059287126_blob.png$ stat $1596059287361_blob.png$ basic statistics $1596059287378_blob.png$ 2 sample t $1596059287392_blob.png$ select summarized data $1596059287349_blob.png$ in sample 1 type 40 in sample size, 5.16 in sample mean, 2.42 in standard deviation $1596059287833_blob.png$ in sample 2 type 40 in sample size, 4.16 in sample mean, 1.58 in standard deviation $1596059287471_blob.png$options $1596059287538_blob.png$ in confidence level type 90 $1596059287387_blob.png$in hypothesized difference type 0 $1596059287578_blob.png$ select the alternative hypothesis as difference $1596059287527_blob.png$ hypothesized difference $1596059287547_blob.png$ ok $1596059287566_blob.png$ok.

to round off any value to needed decimal places :-

right click on the value $1596059477927_blob.png$decimal places $1596059477947_blob.png$ select the needed place(here, we will select 2 )

*** SOLUTION ***

the 90% confidence interval for ($\mu_{1}-\mu_{2}$) is the range from 0.24 hours and 1.76 hours.

interpretation:-

There is 90% confidence that the difference of the means is in the interval.Conclude that there is a signifiacnt difference in the number of leisure hours.(B)

[ as 0 is not included in the interval ]

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