Question

Bullying in schools has been the focus of various programs which work to reduce incidents of bullying and increase the reporting of activity related and/or involving this behavior. A very large school district implemented a new anti-bullying program designed to reduce incidents of bullying. For the past 20 years, the school district has received an average of 370 incidents of bullying across all schools in its district. The data below represent the number of bullying incidents for 15 schools at the end of the first year after implementing the new anti-bullying program: Bullying incidents reported

340 384 370 352 328 348 365 355 335 330 360 376 325 375 368

1. (A) What is the independent variable and its levels?

(B) What is the dependent variable and its scale (i.e., NOIR) of measurement?

B. What is the null hypothesis for the problem described above?

C. Conduct a test of the null hypothesis using p = .05. Be sure to properly state your statistical conclusion.

D. Provide an interpretation of your statistical conclusion from part c.

E. What type of statistical error might you have made?

F. How could the researcher increase statistical power for this study?

G. What is the 95% confidence interval for this study?

H. Provide an interpretation for the interval obtained in part g.

I. How does the confidence interval obtained in part g compare to your statistical conclusion from part c? (i.e., Where does the value expected by the null hypothesis fall in the confidence interval and how does this support or not support your decision to reject or not reject the null hypothesis?)

Answer 1

ANSWER A] ANSWER a: The independent variable is the new anti-bullying program and its level is NOMINAL .

ANSWER b: The dependent variable is incidents of bullying and its scale of measurement is INTERVAL.

ANSWER B] NULL HYPOTHESIS H0: and ALTERNATIVE HYPOTHESIS Ha:

ANSWER C] Test Statistics

The t-statistic is computed as follows:

Decision about the null hypothesis

Since it is observed that t=−3.225<tc​=−1.761, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0031, and since p=0.0031<0.05, it is concluded that the null hypothesis is rejected.

ANSWER D] Interpretation: It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is less than 370, at the 0.05 significance level. The the new anti-bullying program has reduced incidents of bullying.

ANSWER E] REJECTING HO WHEN IT IS TRUE IS TYPE 1 ERROR.

ANSWER F] TO INCREASE STATISTICAL POWER FOR THIS STUDY USE LARGE SAMPLE SIZE.

ANSWER G] 95% CONFIDENCE INTERVAL IS The 95% confidence interval is 343.476<μ<364.664.

ANSWER H] You can be 95% confident that the population mean (μ) falls between 343.476 AND 364.664.

ANSWER I] SINCE the value expected by the null hypothesis DOES NOT fall in the confidence interval therefore SIGNIFICANT.

We can REJECT NULL HYPOTHEISIS