1) A computer is programmed to take the sum of 400 draws made at random with replacement from the box:
(a) What are the lowest and highest possible values for the sum of the 400 draws?
(b) What is the expected value and standard error for the sum of 400 draws?
(c) What is the expected value and standard error for the average of 400 draws?
2) A vice-chancellor of a university was asked to choose a topic for a presidential debate that would soon take place at the university. He organized a poll to determine what support there was for his preferred topic: "the economy". A simple random sample of size 400 was taken from the entire university community of size 100,000. Of those polled, 320 agreed with the vice-chancellor. Find a 95% confidence interval for the percentage of the university community that supported the vice-chancellor.
3) Given the follow set of pairs of data:
x. 6 3 10 11 15
y. 50 80 45 70 60
Compute the actual correlation coefficient.
4.) Given the following data for a math class at this university:
Class semester test average = 82 corresponding standard deviation = 6
Class final exam average = 75 corresponding standard deviation = 8
Correlation coefficient = 0.7
(a) Use this data to write the equation of the regression line in the form y = mx +b where x = semester test grade and y = final exam grade.
(b) Then use the computed regression line equation for this data to predict the final exam test score for a student who had a semester test grade of 85.
5) Among the applicants to one law school in 1976, the average LSAT score was approx. 600, with an SD of 100. These LSAT scores followed the normal curve.
a) What percentage of the applicants scored over 650.
b) Estimate the 80th percentile for the scores.
6) Based on information from Harper's Index 37: out of a simple random sample of 1000 adults 375 claim that they would donate a loved one's organs after death. However, out of another random sample of 1000 adult Americans only 212 claim that they would donate their own organs after death. Does this information indicate the proportion of adult Americans who would donate the organs of loved ones is significantly higher than the proportion who would donate the organs of their loved ones? Use a 5% level of significance in answering your question.
7) A deck of cards contains 52 cards. They are divided into four suits: spades, diamonds, clubs and hearts. Each suit has 13 cards: ace through 10, and three picture cards: Jack, Queen, and King. Two suits are red in color: hearts and diamonds. Two suits are black in color: clubs and spades.
Use this information to compute the probabilities asked for below and leave them in fraction form. All events are in the context that three cards are dealt from a well-shuffled deck without replacement.
a. The first and second cards are both hearts.
b. The third card is an eight.
c. None of the three cards is an ace.
8) Fill in the chart to provide the area (i.e., percentage), width and height of teach class interval.
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Income Range in $1000 units
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Number of families
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% of families
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Width of Class Interval
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Height of Class Interval
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0 to 5
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37
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5 to 10
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58
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10 to 15
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73
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15 to 25
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155
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25 to 35
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150
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35 to 50
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192
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50 to 75
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96
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75 to 100
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39
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9)The average amateur fisherman's catch in past years has been 8.8 Atlantic salmon per day. Suppose that a new quota system restricting the number of fishermen was put into effect this year. A simple random sample of 14 amateur fishermen is taken and the average daily catch for them was computed to be 7.36 Atlantic salmon and the SD of the catches for these 14 amateur fisherman was computed to be 4.03 Atlantic salmon. Use a 5% level of significance in testing the claim that the population average catch is now lower than what it used to be. [Note that this is a small sample and that you may assume the distribution is close to normal.]
10) Out of a simple random sample of 100 adult Americans who did not attend college, 37 believed in extraterrestrials. However, another simple random sample of 100 adult Americans who did go to college indicates that 47 of these believed in extraterrestrials. Does this data indicate that the percentage of people who attend college who believe in extraterrestrials is higher than the percentage of those who did not attend college? Use a 5% level of significance in formulating your answer. Show all work.