1. A scientist claims that a smaller proportion of members of the National Acade
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Question
1. A scientist claims that a smaller proportion of members of the National Academy of Sciences are women when compared to the proportion of women nationwide. Let p1 represent the proportion of women in the National Academy of Sciences and p2 represent the proportion of women nationwide. Which is the correct alternative hypotheses that corresponds to this claim?
A.Ha: p1 - p2 < 0
B.Ha: p1 - p2 > 0
C.Ha: p1 - p2 ? 0
2. Skittles: The popular Skittles candy comes in 5 colors. According to the Skittles website, the colors are evenly distributed in the population of Skittle candies. So each color makes up 20% of the population.
Suppose that we buy 10 small bags of Skittles. For 5 of the bags, we determine the percentage of green Skittles in each bag. For the other 5 bags, we determine the percentage of orange Skittles in each bag. Suppose that each bag contains 40 candies. We define the difference in sample proportions as “green” minus “orange.”
Which sequence of sample differences is the most likely?
A. 0, 0, 0, 0, 0
B. -0.2, 0.225, 0.175, 0.25, -0.225
C. 0, 0.075, -0.125, 0.1, -0.05
3. Every simulation in this module is based on an assumption about the difference between two population proportions. The population proportions affect the mean and the standard error of the differences in sample proportions. The sample size also affects the standard error.
The distribution of differences between sample proportions shown below has mean 0.35, and a standard error of about 0.10.
Which of the following did we use to generate this sampling distribution?
A. Population proportions of 0.85 and 0.65 with samples of size 35.
B. Population proportions of 0.85 and 0.50 with samples of size 35.
C. Population proportions of 0.85 and 0.50 with samples of size 20.
D. Population proportions of 0.85 and 0.65 with sample sizes of 20.
Explanation / Answer
1. (A) Ha: p1 - p2 < 0.
2. (A) 0, 0, 0, 0, 0 (since each color makes up 20% of the Skittles).
3. (A) Population proportions of 0.85 and 0.65 with samples of size 35 (using the formula for standard error).
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