Question

1. Choose the appropriate test for each of the hypotheses below (6 pts in total; 1.5 pts each). [Be sure to watch Ch 15 video first]

Note: It is NOT sufficient to simply answer what the test is. To earn the full point, you need to explain your answer, that is, go through the 3 steps as explained in the video.  

Hypothesis 1 (H1): Participants will indicate a higher intention to donate after they watch the One World: Together At Home event compared to those who do not watch the event. Intention to donate is measured by 7-point bipolar scales.   

H2: Display ad A will retain online users’ attention longer compared to Display ads B or C. Attention is measured by the length of time users stay focused on the ad.  

H3: The less frequent students browse their social media accounts, the more time they will spend studying. The frequency is measured by number of times on a daily basis.

H4: More Californians shop groceries online in April 2020 compared to February 2020.  

2. Compute chi-square statistic (4 pts in total; 2 pts each)

Read this good news to understand the background information for this problem. Since the sample size is stated as 1090 plus I chose 1090. I made up the number of people in the new drug group and placebo group as they were not reported. The cross-tabulation summarizes the test results of the new drug.

Results Treatment	Recovered	Not Recovered	Total
New Drug	414	36	450
Placebo (no new drug)	566	74	640
Total	980	110	1090

1. First, calculate the expected frequency for each cell. Show all the calculations.

Results Treatment	Recovered	Not Recovered	Total
New Drug			450
Placebo (no new drug)			640
Total	980	110	1090

             

2. Then, calculate the chi-square statistic.  Show all the calculations.

     Submission Requirement: Do NOT include my instructions, hypothesis statements, etc. in your submission. Submit your work ONLY.  Use H1, H2, 2A, 2B etc. to refer to the problems.  

Answer 1

Observed frequency:

Results Treatment	Recovered	Not Recovered	Total
New Drug	414	36	450
Placebo	566	74	640
Total	980	110	1090

(A) Expected frequency of each cell

Results Treatment	Recovered	Not Recovered	Total
New Drug	450*980/1090= 404.5872	450*110/1090= 45.4128	450
Placebo (No New drug)	640*980/1090= 575.4128	640*110/1090= 64.5872	640
Total	980	110	1090

To calculate Chi square, we need to follow the following steps.

First calculate (Observed – Expected frequency)2

The table of Observed – Expected frequency

Results Treatment	Recovered	Not Recovered
New Drug	414 – 404.5872 = 9.4128	36-45.4128= -9.4128
Placebo (No New drug)	566-575.4128= -9.4128	74 – 64.5872= 9.4128

(Observed – Expected frequency)2

Results Treatment	Recovered	Not Recovered
New Drug	9.4128*9.4128= 88.6016	(-9.4128*-9.4128) = 88.6016
Placebo (No New drug)	(-9.4128*-9.4128) = 88.6016	9.4128*9.4128= 88.6016

Divide the square by expected frequency. (Observed – Expected frequency)2/Expected frequency

Results Treatment	Recovered	Not Recovered
New Drug	88.6016/404.5872= 0.2190	88.6016/45.4128= 1.9510
Placebo (No New drug)	88.6016/575.4128= 0.1540	88.6016/64.5872= 1.3718

Chi-square = 0.2190+1.9510+0.1540+1.3718= 3.6958 = 3.70