Question

Multi-step Caleulations. For the following items, you will be performing a series of statisica processes, including creation of tables/charts and computation of statistics/parameters. Please carefully read the instructions for each item. Show your work, and clearly indicate your final answer es of statistical MSC1. An office manager has tracked data on the average number of employee complaints hi department receives per week for several years (H-2.4). Recently, corporate policy have not been well-received, and he suspects that the number of complaints that the department eives has increased. He records the number of complaints that came in per week for 8 weeks he policy changes were implemented (M-2.63, SD-1.06). Test the manager's predietion that the number of complaints has increased using a one-tailed test of significance (a -05). a. What type of i-test does this design require? (I point) b. State the null and alternative hypotheses. (1 point) c. Identify the degrees of freedom and critical value(s) of. (1 point) Calculate the appropriate estimate of population variance and the estimated standard error for this test and write your answers in the spaces provided. (2 points) d. estimate of a2 estimated standard error e. Calculate the test statistic and write your final answer in the space provided. (1 point) f. Make a decision: reject or retain the null hypothesis? (1 point) g. Compute an estimate of Cohen's d to measure the size of the effect. (I point) h. Write a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in an APA research report. (2 points)

Answer 1

Part a

This design requires a one tailed/upper tailed/right tailed one sample t-test for population mean.

Part b

Null hypothesis: H₀: The average number of complaints per week is 2.4.

Alternative hypothesis: H_a: The average number of complaints per week is more than 2.4.

H₀: µ = 2.4 versus H_a: µ > 2.4

Part c

We are given sample size = n = 8

Degrees of freedom = n – 1 = 8 – 1 = 7

Level of significance = α = 0.05

Critical value = 1.8946

(by using t-table)

Part d

Estimate of σ² = S² = 1.06^2 = 1.1236

Estimated standard error = S/sqrt(n) = 1.06/sqrt(8)

Estimated standard error = 0.374766594

Part e

Test statistic = t = (Xbar - µ)/[S/sqrt(n)]

t = (2.63 – 2.4)/[1.06/sqrt(8)]

t = 0.23/0.374766594

t = 0.61371532

Part f

Here, we get test statistic value t is less than critical value. So we retain the null hypothesis.

Part g

Cohen’s d = (M1 – M2) / SD = (2.63 - 2.4)/1.06 = 0.216981

Part h

There is insufficient evidence to conclude that the average number of complaints per week is more than 2.4. There is insufficient evidence to conclude that average number of complaints per week is increased.

Cohen’s d is given as 0.216981 which is close to d=0.2 which is considered as small effect size. The sample mean does not differ by 0.22 standard deviations or more.