Question

) Suppose we wanted to evaluate the effect of a diet program on weight loss (in pounds) using four participants. If µ = 19 and σ = 13, and M = 9, conduct a one-tailed Z-test. B) What can we conclude about the effect of this treatment and explain the result clearly in the context of the study.

Answer 1

Solution:

Given: µ = 19 and σ = 13, and M = 9, Sample size = n = 4

Part A) Conduct a one-tailed Z-test

Step 1) State H0 and H1:

Vs

This is left tailed test, since we wanted to evaluate the effect of a diet program on weight loss , so we expected mean weight is less than 19.

Step 2) Test statistic:

Step 3) z critical value:

Level of significance =

look in z table for Area = 0.0500 or its closest area and find z value

Area 0.0500 is in between 0.0495 and 0.0505 and both the area are at same distance from 0.0500

Thus we look for both area and find both z values

Thus Area 0.0495 corresponds to -1.65 and 0.0505 corresponds to -1.64

Thus average of both z values is : ( -1.64+ - 1.65) / 2 = -1.645

Thus Z critical = -1.645

Step 4)  Decision Rule:
Reject null hypothesis ,if z  test statistic value < z critical value = -1.645 , otherwise we fail to reject H0.

Since z  test statistic value = -1.54 > z critical value = -1.645 , we fail to reject null hypothesis H0.

Part B) What can we conclude about the effect of this treatment and explain the result clearly in the context of the study.

Since we failed to reject null hypothesis , we retain H0, thus we do not have sufficient evidence to conclude that: there is significant  effect of a diet program on weight loss.

That is: diet program is ineffective on weight loss