A study was conducted to see the differences between oxygen consumption rates fo
ID: 3218376 • Letter: A
Question
A study was conducted to see the differences between oxygen consumption rates for male runners from a college who had been trained by two different methods, one involving continuous training for a period of time each day and the other involving intermittent training of about the same overall duration. The means, standard deviations, and sample sizes are shown in the following table. Continuous training n_1 = 15 x^bar _1 = 46.28 s_1 = 6.3 Intermittent training n_2 = 7 x^bar_2 = 42.34 s_2 = 7.8 If the measurements are assumed to come from normally distributed populations with equal variances, estimate the difference between the population means, with confidence coefficient 0.95, and interpret.Explanation / Answer
CI = x1 - x2 ± t a/2 * Sqrt(S^2(1/n1+1/n2))
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
Value Pooled variance S^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=46.28
Standard deviation( sd1 )=6.3
Sample Size(n1)=15
Mean(x2)=42.34
Standard deviation( sd2 )=7.8
Sample Size(n2)=7
S^2 = (14*39.69 + 6*60.84) / (22- 2 )
S^2 = 46.035
CI = [ ( 46.28-42.34) ± t a/2 * 6.785 Sqrt( 1/15+1/7)]
= [ (3.94) ± t a/2 * 6.785 * Sqrt( 0.21) ]
= [ (3.94) ± 2.001 * 6.785 * Sqrt( 0.21) ]
= [ -2.275 , 10.155 ]
INTERPRETATIONS
1) We are 95% sure that the interval [ -2.275 , 10.155 ] contains the difference between
true population mean U1 - U2
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the difference between
true population mean U1 - U2
3) Since this Cl does contain a zero we can conclude at 0.05 true mean
difference is zero
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.