Pre-Exam 2 Practice

Which of the below results is an example where a researcher would fail to reject the null hypothesis?

• Caffeine consumption and cortisol levels demonstrated a significant positive correlation.

• Students in class sections where the teacher did not take attendance performed significantly worse than students in class sections where the teacher took attendance.

• There was no significant difference in depressive symptoms between people who reported exercising regularly during quarantine and people who did not report exercising regularly during quarantine.

• Time spent outside per day significantly predicted emotional well-being.

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CCSS.HSS.IC.B.5

A type 1 error is commonly referred to as a false positive and indicates that a significant relationship/difference was incorrectly inferred from results, when no significant relationship should have been concluded. True or False? Explain your decision—why is it true or false? Translate this statement to a “real world” example that illustrates what a Type 1 error is in “real life”.

• True

• False

Tags

CCSS.HSS.IC.B.5

A random sample is important primarily for:

• Generalizability to the population of interest

• Convenience

• Increasing error

• Elimination of confirmation bias

Answer explanation

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CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.3

CCSS.HSS.IC.B.4

Rejecting the null hypothesis, in terms of probability, means that there is a very large probability the difference between groups is due to chance rather than an actual difference. True or False? Explain your decision—why is it true or false?

• True

• False

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.5

A researcher is interested in the number of seconds it takes for mice to complete a maze. The researcher has ten mice run the maze, with the resulting times: 34, 49, 23, 39, 23, 39, 40, 29, 40, 34, and 27 seconds. Calculate the z-score for the mouse who completed the maze the slowest.

Answer explanation

1. 1. mean=33.8

2. 2. std dev=7.98

3. 3. slowest mouse=49seconds

4. 4. Z(slowest)=(49-33.8)/7.98=1.90

Tags

CCSS.HSS.ID.A.4

After collecting this data, the researcher finds another mouse to complete the maze, and finds that this mouse’s time has a z-score of 1.75. How long did it take for this mouse to run the maze, in seconds?

Answer explanation

1.75=(X-33.8)/7.98, X=47.77

A graduate student who works with the researcher in question 1 is interested in the number of seconds hamsters take to complete the same maze used with mice. The distribution of maze times for hamsters had a mean of 56 and a standard deviation of 5. The graduate student’s pet hamster, Bartholomew, had a z-score of -2.4. How many seconds did it take Bartholomew to complete the maze?

Answer explanation

1. 1. mean=56

2. 2. Std Dev=5

3. 3. -2.4=(X-56)/5, X=44

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CCSS.HSS.ID.A.3

CCSS.HSS.ID.A.4

Did Bartholomew complete the maze faster or slower than the average hamster?

• Faster

• Slower

Tags

CCSS.3.MD.A.1

How many standard deviations away from the mean is Bartholomew’s score?

• 2.4 standard deviations below the mean

• 2.4 standard deviations above the mean

Tags

CCSS.HSS.ID.A.4

After collecting data with hamsters, the researcher and graduate student want to compare the times of mice and hamsters to see if an intervention can improve their speed. Should they use the raw scores (i.e., time in seconds) or the z-scores to compare the hamsters and mice?

• Use raw scores

• Use z-scores

• Use both raw scores and z-scores

• Neither

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CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.4