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In: Statistics and Probability

A researcher is curious if age makes a difference in whether or not students make use...

A researcher is curious if age makes a difference in whether or not students make use of the gym at a university. He takes a random sample of 30 days and counts the number of upperclassmen (Group 1) and underclassmen (Group 2) that use the gym each day. The data are below. The population standard deviation for underclassmen is known to be 22.57 and the population standard deviation for upperclassmen is known to be 13.57.

Upper Classmen average = 202.4, population SD = 13.57, n = 30

Under Classmen average = 191.3, population SD = 22.57, n = 30

Is there evidence to suggest that a difference exists in gym usage based on age? Construct a confidence interval for the data above to decide. Use α=0.10. Confidence Interval (round to 4 decimal places):

_____ < μ1 - μ2 < _____

Solutions

Expert Solution

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(184.1449/30 + 509.4049/30)
sp = 4.8082

Given CI level is 0.9, hence α = 1 - 0.9 = 0.1                  
α/2 = 0.1/2 = 0.05, zc = z(α/2, df) = 1.645                  
                  
Margin of Error                  
ME = zc * sp                  
ME = 1.645 * 4.8082                  
ME = 7.909                  
                  
CI = (x1bar - x2bar - tc * sp , x1bar - x2bar + tc * sp)                  
CI = (202.4 - 191.3 - 1.645 * 4.8082 , 202.4 - 191.3 - 1.645 * 4.8082                  
CI = (3.1905 , 19.0095)                  
                  
                  

orchestra answered 1 year ago
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