Question

Consider the following summary statistics, calculated from two independent random samples taken from normally distributed populations.

Sample 1 x¯1=20.87 s21=2.01 n1=16

Sample 2 x¯2=24.00 s22=3.36 n2=15

Test the null hypothesis H0:μ1=μ2against the alternative hypothesis HA:μ1<μ2.

a) Calculate the test statistic for the Welch Approximate t procedure. Round your response to at least 3 decimal places.

b) The Welch-Satterthwaite approximation to the degrees of freedom is given by df = 26.366427. Using this information, determine the range in which the p-value falls:

p-value > 0.10

0.05 < p-value < 0.10

0.025 < p-value < 0.05

0.01 < p-value < 0.025

p-value < 0.01

c) What is the most appropriate conclusion that can be made?

There is sufficient evidence to reject the null hypothesis at both the 5% and 1% level of significance.

There is insufficient evidence to reject the null hypothesis at both the 5% and 1% level of significance.

There is sufficient evidence to reject the null hypothesis at the 5% level of significance, but not at the 1% level of significance.

There is sufficient evidence to reject the null hypothesis at the 1% level of significance, but not at the 5% level of significance.

Answer 1

a)

test statistic t =-5.294

b)

p-value < 0.01

c)since p value is less than 0.05 and 0.01 :

There is sufficient evidence to reject the null hypothesis at both the 5% and 1% level of significance.