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 30 days.
researchers counted the number of occasions when students from both groups arrived late 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 used the following table, which summarizes the results of 1000 randomizations of the data with differences of means rounded to the nearest 5 points.
consider the significance level is set at 5%, so results lower than 5% can be considered statistically significant.
table showing differences in means and their frequencies
part a
calculate 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 blank, which is blank 5%.
the result is blank.

Explanation:

Step1: Identify relevant data

The experiment has 1000 randomizations. We want to find the probability of the treatment - group mean being 15 points or more less than the control - group mean.

Step2: Sum frequencies for relevant differences

We sum the frequencies for differences of - 15, - 20, - 25, etc. From the table, the frequencies for differences of - 15, - 20, - 25 are 48, 17, 12 respectively. The sum of these frequencies is \(48 + 17+12=77\).

Step3: Calculate probability

The probability \(P\) is the sum of relevant frequencies divided by the total number of randomizations. So \(P=\frac{77}{1000} = 0.077\).

Answer:

The probability of the treatment - group mean being 15 points or more less than the control - group mean is \(0.077\).