Question

question 2 according to a research study, people can better manage their time when they wear watches than when they use mobile phones or other gadgets to keep track of time. to test the studys results, researchers randomized 300 college students into a treatment group and a control group. the treatment group was asked to wear a watch every day, and the control group was asked to avoid wearing a watch for 50 days. researchers noted the number of occasions when students from both groups arrived later than their scheduled time. the results of the experiment showed that the mean score of the treatment group was exactly 15 points less than the mean score of the control group. to test whether the results could be explained by random chance, the researchers created the following table, which summarizes the results of 1,000 randomizations of the data with differences of means rounded to the nearest 5 points. consider the significance level to be set at 5%, so results lower than 5% can be considered statistically significant. treatment group mean - control group mean frequency -25 10 -20 18 -15 50 -10 127 -5 195 0 226 5 180 10 117 15 48 20 17 25 12 part a question determine the probability of the treatment groups mean being lower than the control groups mean by 15 points or more. then complete the statements. the significance level is set at 5%, and the probability of the result is %, which is the significance level. the result is

Explanation:

Step1: Identify relevant frequencies

We want to find the probability of the treatment - group's mean being lower than the control - group's mean by 15 points or more. So we consider the frequencies for differences of - 15, - 20, and - 25. The frequencies are 50, 18, and 10 respectively.

Step2: Calculate total relevant frequency

The total relevant frequency is \(50 + 18+10=78\).

Step3: Calculate probability

The total number of randomizations is \(n = 1000\). The probability \(P\) is given by the formula \(P=\frac{\text{total relevant frequency}}{\text{total number of randomizations}}\). So \(P=\frac{78}{1000}=7.8\).

Answer:

The significance level is set at 5%, and the probability of the result is \(7.8\%\), which is greater than the significance level. The result is not statistically significant.