GKT101: General Knowledge for Teachers – Math

1. A researcher wanted to check whether marriage causes people to become more responsible. Specifically, he was interested to know if marriage causes people to become more careful drivers.

He went over the files of all car accidents that occurred in the past 3 years in his state, and he calculated how many accidents out of the total number of accidents were caused by married people. Then, he compared his results with the actual percentage of married people in his state.

What type of statistical study did the researcher use?

Choose 1 answer:

(A) Sample study

(B) Experiment

C) Observational study

Is the study appropriate for the statistical questions it's supposed to answer?

Mark the most suitable choice.

Choose 1 answer:

(A) Yes, because he compared the percentage of accidents caused by married people to the percentage of married people in general.

(B) No, because he didn't use a sample of the car accident files.

(C) No, because it doesn't allow the researcher to show that marriage causes careful driving.

(D) Yes, because causing accidents is a very good measure of careless driving.

2. Scientists interested in the effect of exercise on the duration of sleep conducted the following study: $180$ overweight men were randomly assigned to two groups. One group was instructed to perform aerobic exercise for about an hour per day, and the other group was instructed to continue with their exercise-less routine.

The sleep duration of each subject was measured at two points: before the randomization and $10$ weeks after it. Then, the scientists calculated the change in sleep duration for each subject, where a positive value means the duration increased, and a negative value means it decreased.

What type of a statistical study did the scientists use?

Choose 1 answer:

(A) Sample study

(B) Experiment

(C) Observational study

The scientists found that the mean change in sleep duration of the group who exercised is $65$ minutes greater than the mean change of the group who didn't. Based on some re-randomization simulations, they concluded that the result is significant and not due to the randomization of the groups.

What valid conclusion can be made from this result?

Mark the most suitable choice.

Choose 1 answer:

(A) The result suggests a positive correlation between daily exercise and sleep duration among overweight men.

(B) The result suggests that people who exercise daily sleep better than people who don't.

(C) The result suggests a positive correlation between daily exercise and sleep duration.

(D) The results suggest that adopting an exercise regime may increase sleep duration among overweight men.

3. Vishal was interested in the relationship between a person's age and their musical preferences. He called all the numbers listed in his city's telephone directory, and whenever someone answered and agreed to be surveyed, he asked them for their age and interviewed them about their musical preferences.

Once he was done, he analyzed his results and found that younger people prefer pop and hip-hop music while older people prefer jazz and classical music.

What type of statistical study did Vishal use?

Choose 1 answer:

A) Sample study

(B) Experiment

(C) Observational study

Is the study appropriate for the statistical questions it's supposed to answer?

Mark the most suitable choice.

Choose 1 answer:

(A) Yes, because the results he got sound very reasonable.

(B) No, because he only interviewed people who agreed to it.

(C) Yes, because he called all the numbers in the city's directory.

(D) No, because there was no control group or treatment group.

4. Researchers were interested in assessing the effect of meditation on work stress. They randomly assigned $200$ full-time employees to two groups. One group was instructed to meditate $10-20$ minutes twice per day, and to participate in weekly 1-hour sessions, while the other group wasn't given any special instructions.

Just before the randomization and also after a period of $8$ weeks, all participants were required to fill out the Psychological Strain Questionnaire (PSQ), an accepted measure of work stress. The researchers calculated the difference in questionnaire scores for all participants, where a positive change corresponds to a reduction in work stress. Then, they compared the average differences of each group.

What type of a statistical study did the researchers use?

Choose 1 answer:

(A) Sample study

(B) Experiment

(C) Observational study

The researchers found that the mean change in PSQ scores of the group who meditated is $21$ points greater than the mean change in PSQ scores of the group who didn't. Based on some re-randomization simulations, they concluded that the result is significant and not due to the randomization of the groups.

What valid conclusions can be made from this result?

Mark the most suitable choice.

Choose 1 answer:

(A) The result suggests a positive correlation between meditation and work stress reduction.

(B) The result suggests that meditation can reduce stress.

(C) Meditation reduces work stress.

(D) The result suggests that meditation can reduce work stress.