Question

Using a = 0.05, test if the mean weight change is less than 0 if a sample of size 25 people on the Atkins diet yielded a mean change of -2.1 and a sample std dev of 4.0.

Answer 1

Solution:

Step 1) State H0 and H1:

Since we have to test if the mean weight change is less than 0 , this is left tailed test.

Thus:

Vs  

Step 2) Test statistic:

Step 3) Critical value:

df = n - 1 = 25 - 1 = 24

One tail area = level of significance = 0.05

t critical value = -1.711

( its negative , since this is left tailed test)

Step 4) Decision Rule:

Reject null hypothesis H0, if t test statistic value < t critical value = -1.711 , otherwise we fail to reject H0

Since t test statistic value = < t critical value = -1.711 , we reject null hypothesis H0.

Step 5) Conclusion:

At 0.05 level of significance, we have sufficient evidence to conclude that: the mean weight change is less than 0.