A complete answer for probability problems such as those found in Problems 1 and 4 must include an interpretive sentence relating the probability to the text of the problem in order to receive full credit.
- 9 points. The distribution of SAT exam scores is approximately normal with m = 500 and s = 100. For the population of students who have taken the SAT,
- 3 points. What proportion of students has SAT scores between 420 and 540?
3 points. What is the percentile rank of someone who scores a 650?
3 points. To be considered for a scholarship at State of Confusion College of University Studies, a student must be in at least the 40th percentile of all SAT test takers. What is the lowest SAT score that will be considered for a scholarship?
6 points. As mentioned previously, the distribution of ACT scores is approximately normal with m = 20 and s = 5.
2 points. If you selected a random sample of n = 90 scores from this population, how much error would you expect between the sample mean and the actual population mean (i.e., what is the standard deviation of the sampling distribution σ or the standard error)?
2 points. If you selected a random sample of n = 900 scores, how much error would you expect between the sample mean and the actual population mean?
2 points. How much error would you expect for a sample of n = 9000 scores?
1 point. Which of the following statements is not true?
- The mean of the sampling distribution of sample means will always be equal to the population mean regardless of the shape of the distribution.
- The standard error is always smaller than the standard deviation except when our sample is n = 1.
- The Unit Normal Table can only be used when the distribution of scores in the population is approximately Normal.
18 points. Using imaginary data from this class, we can say that the population distribution of scores is approximately Normal with a mean score (µ) on the midterm of 84.75 and a standard deviation (σ) of 8.4. If I were to take a random sample of size n = 36, what is the probability that the sample mean is:
5 points. Higher than 86.85?
8 points. Between 83 and 86.85?
5 points. Less than 83?
Extra Credit 1 point. Briefly show that we would be more likely to get a sample mean higher than 81.95 if my sample size (n) was 64 instead of 36 if the population mean and standard deviation remain the same.
16 points (From Frankfort-Nachmias and Leon-Guerrero, 2002) For each of the following situations state the null and research hypotheses. Pay attention to whether these should be constructed as a one –tailed or a two-tailed test.
4 points Researcher A is interested in finding out if the average income of elementary school teachers is different from the national average income for adults. According to recent census information, the average income for adults age 25 and older is $40,000.
4 points Researcher B believes that students in small liberal arts colleges attend more parties per month than students nationwide. Previous research has shown that nationally, undergraduate students attend an average of 2.5 parties per month.
4 points Researcher C thinks that stress (measured on an “interval” scale from 0-100, 0 being non-existent and 100 being extremely high) will be lower for adults who own dogs (or other pets) than for the general adult population. The population mean (µ) of the general population is 50.
4 points Make up your own research scenario where Researcher D will use a one-tailed hypothesis. No more than 50 words, but descriptive enough that it is clear what the hypothesis structure must be. Include the hypotheses that are implied by your research scenario.
