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Question

~~A survey asked students if they preferred to sit in the front, middle, or back of the class and also asked them their heights.  The following data are the heights for 15 female students who said they prefer to sit in the back of the class.

68, 62, 65, 69, 68, 69, 64, 66, 69, 68, 62, 64, 67, 68, 65

The mean height for the population of college females is 65 inches.  Test the claim that the mean height for females who prefer to sit in the back of the room is higher than it is for the general population.  In other words, test whether females who prefer to sit in the back of the room are taller than average.  Use alpha = 0.05.

Answer 1

Sample mean is 66.27". Variance=5.66". SD=2.38". Pop mean=65".
Standard error of the mean=2.38/sqrt(n)=0.6144, where n=15.

Degrees of freedom (df)=14 (n-1, where n=sample size of 15)

Alpha=0.05 (95% confidence), t=2.145

The population mean lies between 66.27-2.145*0.6144=64.95 and 66.27+2.145*0.6144=67.49 if the claim is unsupported, i.e., the pop mean is included in the range for the sample mean. It's clear from these figures that the pop mean of 65" is just about included in the range, implying that the tallest females are not necessarily sitting at the back. The sample mean is not significantly different from the population mean.