A sociologist claims that sleeping time of children ages 12-14 in 1981 is different from that...

A sociologist claims that sleeping time of children ages 12-14 in 1981 is different from that of children ages 12-14 today. A study was conducted in 1981 to find the time that children ages 12-14 with samplse size of 22. Recently, similar study was conducted with sample size of 20. Summary of the sleep time comarison is given below. Use α = 0.01 to perform the analysis.

  data:  sleep_1981 and sleep_now
  t = -8.7477,  p-value = ......
  alternative hypothesis: true difference in means is not equal to 0
  99 percent confidence interval:

   -1.6238202 -0.8561798
  sample estimates:
  mean sleep time 1981 mean sleep time recently

7.75 8.99

(a) Which test is reasonable to use? Indepenpaired t-test or paired t-test? Defend your choice.
(b) State the null and alternative hypothesis.
(c) Circle one: One Tail Test / Two Tail Test.
(d) Illustrate graphically the rejection region.
(e) Find the p-value for the test statistic. Use table.

(f) Give the significant statement for the hypothesis test. Make sure to connect your result with the story of question for full credit.

(g) Find 99% confidence interval and interpret it in the context of the question. Pay extra attention to the signs of lower and upper limits of confidence interval. Does it reveal more about the comparisons of these data?

Solutions

Expert Solution

(a) Since two samples of sleeping time of children ages 12-14 in 1981 and children ages 12-14 today hence these two samples are independent hence we use 2 sample t test or Independent paired t-test.

(b)

(d) Under null hypothesis, test statistic follows t-distribution with degrees of freedom=22+20-2=40

There is sufficient evidence that sleeping time of children ages 12-14 in 1981 is different from that of children ages 12-14 today. Hence we accept the claim.

(g) 99% C.I. is ( -1.6238202 -0.8561798)

Since this C.I. does not contain zero hence we are 99% confident that sleeping time of children ages 12-14 in 1981 is different from that of children ages 12-14 today. Moreover since the C.I. contains only negative values so we are 99% confident that sleeping time of children ages 12-14 in 1981 is less than that of children ages 12-14 today.

milcah answered 9 months ago

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