Question

Onsider the following hypothesis test.

:
:
The following results are for two independent samples taken from the two populations.
Sample 1 sample 2
n1=45 n2=55
x1=25.5. x2=22.6
o1=5.0 02=6.0
a. what is the value of the test statistic (n round to 2 decimals)?
b. what is the p-value ( run to 4 decimals)? use z-value rounded to 2 decimals places.
c. with a= 0.05, what is you hypothesis testing conclusion?


a. What is the value of the test statistic (round to 2 decimals)?

Answer 1

To find the value of the test statistic, we need to calculate the standard error of the difference between the means and then use it to calculate the z-score.

The formula for the standard error of the difference between the means is:

SE = sqrt((s1^2/n1) + (s2^2/n2))

where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Substituting the given values, we get:

SE = sqrt((5^2/45) + (6^2/55)) = 1.257

The formula for the z-score is:

z = (x1 - x2) / SE

Substituting the given values, we get:

z = (25.5 - 22.6) / 1.257 = 2.31

Therefore, the value of the test statistic is 2.31