## PSYC 201 Statistics

__Question #1 __

Joe and Katy are enrolled in a psychology course. In this course, the average grade is 71 and the variance of the grades is 81. Assume that the grades are perfectly normally distributed.

- Joe’s final grade was 53. What percentage of students in the course had a grade lower than Joe?

- Katy had a final grade that was 1 standard deviation above the mean. What was her final grade?

- What percentage of students in the course had a higher grade than Katy?

- What percentage of students in the course had a grade in between Joe and Katy?

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__Question #2 __

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In a recent survey, UVic students were asked to rate their opinions of “Cheese” pizza and “Pepperoni” pizza. The ratings were on a “1” to “10” scale where “1” indicates a strong negative opinion and “10” indicates a strong positive opinion. The histograms of the ratings are shown below:

- Compute and report the range, mean, median, and mode of the Cheese pizza ratings

- Compute and report the range, mean, median, and mode of the Pepperoni pizza ratings

- Do you think the two histograms show equal or unequal variability? Why or why not? (Hint: See variance formula below.)

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__Question #3 __

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Imagine a researcher is interested in whether psychology majors are better at recognizing facial expressions than computer science majors. The *t-test* formula (shown below) is the inferential statistic for determining whether this experiment produced “significant” difference between the two groups.

As a general rule, an experimenter would like to obtain a large *t* score that is greater than 1.96. What are the three factors that determine the magnitude (size) of the *t* score?

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__Question #4 __

Austin is a student in the Psych 201 course. Based on personal observations, Austin thinks that left-handed individuals have a larger reading vocabulary than right-handed individuals. To test this hypothesis, Austin administered the North American Adult Reading Test (NAART) to a group of university self-identified left- and right-handed students. The NAART is comprised of 50 written English words which all have atypical spellings (e.g., “aisle”, “chord”, “gauge”). Previous research has indicated that performance on the NAART predicts reading ability and general verbal intelligence.

4a.) State the research (alternative) and null hypotheses in Austin’s study.

4b.) Austin averages the scores and finds that the mean score for the left-handed group was 85% correct and the mean sore for the right-handed group was only 65% correct. Should Austin conclude that the left-handers are statistically better than the right-handers in their reading vocabulary? Why or why not? Please give a complete explanation for your answer.

4c.) Draw one diagram showing where the 20% mean score difference between the left-handed and right-handed groups is significant. Explain why the diagram shows a significant difference between the two groups.

4d.) Draw another diagram where the mean score difference of 20% between the left-handed and right-handed groups is **not** significant. Explain why the diagram shows that the difference is not significant.

4e.) State and explain the Type 1 and Type 2 errors that Austin might commit in the reading study.