test statistic help

Question

Testing:

H0:μ=44.6

H1:μ<44.6

Your sample consists of 46 subjects, with a mean of 44.3 and standard deviation of 1.01.

Calculate the test statistic, rounded to 2 decimal places.

t=

Answer 1

This is a directional, one-tailed t-test. You can tell this is one-tailed because the alternative states the mean will be BELOW 44.6, rather than just different. Because you only have one sample, you know this a one-sample t-test. The equation for a one sample t-test is:

xbar - mu / standard error.

or in words: the sample mean minus the null mean, divided by standard error (SE).

In this case, standard error = S/√N. This means the standard deviation S divided by the square root of the sample size N.

So for this problem.

xbar = 44.3

MU = 44.6

S = 1.01

N = 46

SE = 1.01/√46

t = (44.3 - 44.6)/SE

I hope that is helpful!