Question

Please use the following information to answer 3a-3e:

A random sample is selected from a normal population with a mean of µ = 30 and a standard deviation of σ= 8. After a treatment is administered to the individuals in the sample, the sample mean is found to be x̅ =33.

Furthermore, if the sample consists of n = 16 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05.

3a. Which of the following correctly represents the null and alternative hypothesis for the mentioned sample of n =16 (MUST SHOW WORK FOR THIS PROBLEM)?

		Ho: µ ≥ 30 H1:µ < 30
		Ho: µ = 30 H1:µ ≠ 30
		Ho: µ ≤ 30 H1:µ > 30
		Ho: µ > 30 H1:µ ≤ 30

3b. Which of the following represents the critical region for this mentioned sample (MUST SHOW WORK FOR THIS PROBLEM)?

		z = 1.65
		z = -1.96
		z = ±1.96
		z = ±1.65

3c. Compute the test statistic(z-observed) for the mentioned sample (MUST SHOW WORK FOR THIS PROBLEM).

Note: Must show calculations for standard error alongside the calculations for the test statistic.

3d. Based on the calculated test statistic, would you reject the null hypothesis established in question 3a (MUST SHOW WORK FOR THIS PROBLEM)?

Yes
No

3e. Based on the previously conducted steps, we can conclude (MUST SHOW WORK FOR THIS PROBLEM):

		The treatment significantly increases scores.
		The treatment significantly decreases scores.
		The treatment has a significant effect.
		The treatment does not have a significant effect

Answer 1

3a. Correct answer: Option(B)

Ho: µ = 30

H_1:µ ≠ 30

3b. Correct answer: option (C)

z = ±1.96

3C.

3d. Correct answer: NO

since Z value is in Z critical values so we accept H₀

3e) Correct answer: The treatment does not have a significant effect