The confidence Interval limits include 0 which suggests that the two population
ID: 3229895 • Letter: T
Question
The confidence Interval limits include 0 which suggests that the two population means are unlikely to be equal. There appears to be a significant difference between the mean amount of time spent watching television for women and the moan amount of time spent watching television for men. Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal (sigma_1 = sigma_2), so that the standard error of the difference between means is obtained by pooling the sample variances. A researcher was interested in comparing the amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows Construct a 99% confidence interval for mu_1 - mu_2, the difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men. A) -7.25 hrsExplanation / Answer
I don't thing it will require using ti84
the 95% confidence interval for population mean difference (1 - 2 ) is =
(x1-bar - x2-bar ) +- t/2, n1 +n2 -2 * sp * sqrt [ 1/n1 + 1/n2 ]
where
x1-bar = 12.7 hr; x2-bar = 16.7hr
= 0.05 and n1 = 14 and n2 = 17
sp2 = [(n1 - 1) s12 + (n2 -1) s22]/ (n1 +n2 -2)] = [ (13 * 4.32 + 16 * 4.92 )/29 = 21.5355
for dF = 29 and alpha = 0.05
t0.05,29 = 2.045 (only this value you require to calculate form ti 84 calculator where you can use t - value chart in that calculator and put dF and alpha level and get values of critical t.
(x1-bar - x2-bar ) +- t/2, n1 +n2 -2 * sp * sqrt [ 1/n1 + 1/n2 ]
= (12.7 - 16.4) +- 2.045 * sqrt (21.5355) * sqrt [ 1/14 + 1/17]
= -3.7 + 2.045 * 4.64 * 0.361 = ( -7.1254, -0.2745)
C is the correct answer.
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