Small Sample Test Statistic: Mean

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Concept #1: Calculating the Small Sample Test Statistic of a Sample Mean

Concept #2: Calculating the Small Sample Test Statistic of a Sample Mean: Intro

Practice: A car company would like to see if a particular model holds up to the claim that its efficiency is 42 mpg. A 
random sample of 25 cars is taken. The mean was 40 with a standard deviation of 15. Test to see if the mpg of the sample 
is different from the claimed 42 mpg. Test using an α = .05.

Practice: Professor Renzo is said to teach Statistics better than others. Students are all given the same tests for their 
final exam. On average, students score a 72 on this final exam. 16 randomly selected s tudents from Renzo’s class revealed 
a mean and standard deviation of 80 and 6, respectively. Can we say that Renzo’s students performed better than average 
using a 1% significance level?

Practice: Professor Blah is said to teach Statistics worse than others. Referring to Practice 2, if 25 randomly selected 
students from Blah’s class reveal a mean and standard deviation of 65 and 50, respectively, is there enough evidence to 
say that Blah’s students scored lower than the established average? Use α = .01.