TAKE IT HOME Most children enjoying watching television, but child psychologists

Question

TAKE IT HOME Most children enjoying watching television, but child psychologists are concerned that watching three hours or more of television per day negatively impacts a child's ability to sleep. The amount of time a person sleeps is called sleep duration Consider the following independent samples. Sample 1 has the sleep durations of 14 children who watched television for three hours or more on a given day. The mean sleep duration for this sample was 6.78 hours with a standard deviation of 0.63 hours. Sample 2 has the sleep durations of 18 children who watched television for less than three hours on a given day. The mean sleep duration for this sample was 7.44 hours with a standard deviation of 1.05 hours. Researchers have determined that these populations are normal. Can we conclude at the 5% significance level that children who watch more than three hours of television get less sleep than children who watch less than three hours of television?

Explanation / Answer

QUestion 13

(A) Margin of error = Critical test statistic * Standard error of difference

Critical test statisitc = tdf,0.05 = t28,0.05 = 2.0484

Standard error of difference se0 = sqrt [s12/n1 + s22 /n2] = sqrt [0.632 /14 + 1.052/18] = 0.2993

Margin of error MOE = 2.0484 * 0.2993 = 0.6132

(B) Here 95% confidence interval = (x1 - x2 ) +- MOE = (6.78 - 7.44) +- 0.6132

= -0.66 +- 0.6132

= (-1.273, - 0.047)

(C) Here confidenceinterval is consistent with the hypothesis test results.

(D Here we can interpret the confidence interval that there is if we take same sample size for each group then difference between sleep hours between two groups has the 95% probability to come inbetween the given values.

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