Questions 1-2, for atleast one problem, complete all calculations by hand using
ID: 3222196 • Letter: Q
Question
Questions 1-2, for atleast one problem, complete all calculations by hand using the appropriate z or t formula. The other problems can be completed using a graphing calculator or StatCrunch. Select type of Confidence Interval, check requirements, calculate E, construct Confidence Interval & write in interval notation, and interpret CI in context of origional the problem.
Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent and that they have been randomly selected from normally distributed populations. Do not assume that the population standard deviations are equal.
1) A researcher was interested in comparing the amount of time spent watching television by women and 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 TV during the previous week. The summary staistics are below. Construct a 99% confidence interval for u1 - u2, the difference between the mean amount of time spent watching TV for women and the mean amount of time spent watching TV for men.
2) The mean white blood cell counts of 40 randomly selected women is 7.15 (1000 cells/uL) with a standard deviation of 2.28. Construct a 99% confidence interval estimate of the mean white blood cell count for the population of women.
WOMEN MEN n1=14 n2=17 x1=12.8 hrs x2=14.0 hrs s1=3.9 hrs s2=5.2 hrsExplanation / Answer
Q1.
CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=12.8
Standard deviation( sd1 )=3.9
Sample Size(n1)=14
Mean(x2)=14
Standard deviation( sd2 )=5.2
Sample Size(n2)=17
CI = [ ( 12.8-14) ±t a/2 * Sqrt( 15.21/14+27.04/17)]
= [ (-1.2) ± t a/2 * Sqrt( 2.677) ]
= [ (-1.2) ± 3.012 * Sqrt( 2.677) ]
= [-6.1281 , 3.7281]
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