Question

A student wonders if people from small towns are friendlier than the general population. To test this hypothesis he gives 100 people a friendliness survey. The population mean for this survey is 50 with a standard deviation of 12. The mean for his sample is 52.5. Compute a z for a sample mean to determine if his hypothesis was supported. Use α = .05, one tailed. Which of the following statements describes a Type I error in the context of this study?

a) concluding that people in small towns are friendlier than the general population when they are not friendlier

b) concluding that people in small towns are not friendlier than the general population when they are not friendlier

c) concluding that people in small towns are friendlier than the general population when they are friendlier

d) concluding that people in small towns are not friendlier than the general population when they are friendlier

Answer 1

here null hypothesis :

H0 : People from small towns are friendlier than the general population

z = (52.5-50) / (12 / (500.5) ) = 1.473

z critical value (α = .05) = 1.645

1.473 < 1.645

therefore the hypothesis is supported

A Type 1 error occurs when the null hypothesis is true, but we reject it because of an usual sample result.

by this definition of type 1 error the type 1 error is described as :

d) concluding that people in small towns are not friendlier than the general population when they are friendlier

P.S. (please upvote if you find the answer satisfactory)