Question

Suppose that Raven studied for the Graduate Management Admission Test (GMAT) using a well-known preparation class and was thrilled to receive a total score of 770. Her friend Eric, however, thinks she would have scored just as well without the class.

To test the efficacy of the class, they obtain a small but random sample of 19 test results from other students using the same class. This sample's average is 568.56 with a standard deviation of 116.72. In comparison, the national average was 550.12. Assume the population's results are normally distributed but that its standard deviation is not known.

Raven and Eric decide to perform a two-tailed ?t‑test at a significance level of ?=0.05α=0.05. How many degrees of freedom should they use in their calculations?

df=

Lucy is using a one-sample ?t‑test based on a simple random sample of size ?=31n=31 to test the null hypothesis ?0:?=15.000H0:μ=15.000 cm against the alternative ?1:?<15.000H1:μ<15.000 cm. The sample has mean ?⎯⎯⎯=15.106x¯=15.106 cm and standard deviation is ?=1.053s=1.053 cm.

Determine the value of the ?t‑statistic for this test. Give your answer to three decimal places.

t =

Answer 1

1) n = sample size = 19

d.f = n -1 = 19 - 1

d.f = 18

2)

test statistic t = (xbar - )/(s/√n)

t = (15.106 - 15)/(1.053/√31)

t = 0.560