Because of the coronavirus crisis, Mr. Adkins AP statistics classes are now involved in remote learning, and Mr. Adkins is worried that the proportion of assignments that are completed and on time has decreased. To see if this is true, Mr. Adkins randomly selects 50 student assignments from before the remote learning began and randomly selects 50 student assignments from after remote learning started. He finds that 37 of the assignments from the traditional school group were completed and on time, while only 30 of the assignments from the remote learning group were completed and on time. Use this information to answer the following questions.
(e) Identify the explanatory and response variables in Mr. Adkins’ study. Explanatory: Response:
(f) Was Mr. Adkins’ study an observational study or an experiment? Explain.
(g) Describe a method by which Mr. Adkins could use a matched pairs design to improve his study.
(h) Mr. Adkins wants to use the results of his study to construct a 95% confidence interval for the difference in the proportion of assignments completed and on time for the traditional school group and the remote learning group. Confirm that all appropriate conditions have been satisfied.
(i) The confidence interval from part (g) is calculated to be (-0.0423, 0.3223). Interpret the results of this confidence interval in the context. Based on the results of this confidence interval do you believe there is convincing evidence that the proportion of students turning in assignments complete and on time has decreased since remote learning began?

(f) Mr. Adkin's study was an observational study. This was because Mr. Atkin was not manipulating the Type of learning (Traditional school, Remote learning) to study its effect on the assignments which are completed and on time. Mr Atkin was not conducting an experiment but he was only collecting relevant information.

(g) Mr. Adkin can use a matched pair design through the following steps:

Step 1: Identify the set of 50 students.

Step 2: Conduct a Traditional school on set of the 50 students.

Step 3: Conduct Remote learning on the set of 50 students.

Step 4: Collect information on the assignments which are completed and also on time for the Traditional school and the Remote learning.

Step 5: Conduct a Hypothesis Test in order to find out whether the assignments which are completed and also on time has reduced significantly.

h. Appropriate conditions that have been satisfied as follows:

(i) The sampling method for each population is the simple random sampling.

(ii) The samples are independent

(iii) Each sample consists of at least 10 successes and also 10 falures

(iv) Each population is at least as 20 times as large as the sample.

(i) The 95% confidence interval (-0.0423,0.3223) shows a range of values that we are 95% confident would contain the true unknown population mean of the assignments completed.

Since the confidence interval (-0.0423,0.3223) includes 0, this denote that there is no convincing evidence that proportion of students turning in assignments complete and also on time has decreased.