Math 120
Review Questions
Chapters 1, 2, and 3
(These provide additional review, but you should also review exercises, class notes and do suggested exercises from the text)
- “Do you agree that the freeze on tuition fees should be lifted in B.C.?
A television program asked its viewers to call in with their opinions on that question. There were 18,600 callers of whom 97% said “no” and 3% answered yes. A provence-wide random sample of 500 adults from B.C. found that 55% answered “no”, 30% “yes” and 15% “not sure” to the same question.
a)Which of these is likely to give the best guide to the true feelings of the people in B.C.? Explain.
b)Identify the sample and the population for the second study (the 55% “no” study).
2. A random sample of 7 out-of-province tourists was surveyed in Kamloops last summer. Each was asked how many days they planned to spend in British Columbia. Their answers are listed below
12337245210
For these observations, find the:
a)mean
b)median
c)Q1______Q3______
d) standard deviation
d)Other than the number of days they plan to spend in British Columbia, think up two other variables that the tourists might have been asked about. In particular, give:
i)1 quantitative variable of your choice
ii)1 categorical variable or your choice
- As part of a market research study, a random sample of 30 Kamloops residents were asked approximately how much money they spent in restaurants in the past month. The results (in dollars) are given below:
006881212202020
25253030343535354042 45 45 45 45 50 55 55 75 100 500
a)give the five-number summary for these data.
b)draw a carefully labeled box plot. (dollars spent is along the horizontal axis)
c)Suppose the highest observation was $105 instead of $500.
i) Would this cause the median to change?
ii) Would this cause the mean to change?
iii) In this case, do you think the mean or the median is better representation of a “typical” value from the sample? Why?
- An instructor asked a random sample of 6 students to record their study times in a first-year Stats course. At the end of 2 weeks the students wrote a test. The following is a table showing the total hours studied, x and the test score, y.
Hours studied (x):10151220816
Test Score (y):728874846175
For these data: x = 13.50 sx = 4.37 y = 75.67 sy = 9.52
r = 0.8028
a)Plot the data in a scatter plot
b)Find the equation of the least-squares regression line. (Use four decimal places for the slope and two decimal places for the y-intercept.)
c)Predict the test score obtained by a student who studies 13 hours.
d)The value of r2 is 0.644. Explain what this means for this particular problem.
- The weights of East-Manitoban Talking Beetles is normally distributed with a mean of 7.20 pounds and a standard deviation of 1.20 pounds. A beetle has just jumped on your back.
a)What is the probability that the beetle weights between 6 and 8 pounds? Shade in the corresponding areas on the graphs.
b)The beetle says he is one of the smallest 8% of beetles in the terms of weight. What is the most the beetle could weigh? Shade the area corresponding to the smallest 8% on the graphs.
- Before the introduction of the Salk vaccine in the early 1950’s, investigators looked at the relationship between polio and soft drink sales. It was found that in months where more pop was sold there were more cases of polio, and in months where less pop was sold there were fewer cases of polio.
a)Is this an experiment? Why or why not?
b)Is the correlation between soft drink sales and new polio cases positive, negative or 0?
c)Does this show that drinking pop makes you more likely to get polio? Explain? (hint: polio stuck more commonly in the summer)