STAT 200 week 7 homework
Week 7 Homework
Lane et al.
Chapter 14
Page 512 #2
2. The formula
for a regression equation is Y’ = 2X + 9.
a. What would be the predicted score for a person scoring 6 on X?
b. If someone’s predicted score was 14, what was this person’s score on X?
Page 512 #6
6. For the X,Y data below, compute:
X Y
4 6
3 7
5 12
11 17
10 9
14 21
a. r and determine if it is significantly different from zero.
b. the slope of the regression line and test if it differs significantly from zero.
c. the 95% confidence interval for the slope.
Chapter 17
Page 614 #5
5. At a school pep rally, a group of sophomore students organized a free raffle forprizes. They claim that they put the names of all of the students in the school inthe basket and that they randomly drew 36 names out of this basket. Of the prizewinners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 wereseniors. The results do not seem that random to you. You think it is a little fishythat sophomores organized the raffle and also won the most prizes. Your school iscomposed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors.
a. What are the expected frequencies of winners from each class?
b. Conduct a significance test to determine whether the winners of the prizeswere distributed throughout the classes as would be expected based on thepercentage of students in each group. Report your Chi Square and p values.
c. What do you conclude?
Page 617 #14
14. A geologist collects hand-specimen sized pieces of limestone from a particulararea. A qualitative assessment of both texture and color is made with thefollowing results. Is there evidence of association between color and texture forthese limestones? Explain your answer.
COLOUR
TEXTURE LIGHT MEDIUM DARK
FINE 4 20 8
MEDIUM 5 23 12
COURSE 21 23 4
Illowsky et al.
Chapter 11
Page 614 #70
70. True/False: The standard deviation of the chi-square distribution is twice the mean.
Page 621
For each word problem, use a solution sheet to solve the hypothesis test problem. Go to Appendix E for the chi-square solution sheet. Round expected frequency to two decimal places.
102. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown inTable
Conduct a test for homogeneity at a 5% level of significance.
French Toast Pancakes Waffles Omelettes
Men 47 35 28 53
Women 65 59 55 60
Page 623
Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.
113. df= ________
117. Let α= 0.05
Decision: ________
Conclusion (write out in a complete sentence.): ________
Chapter 12
Page 677 #66
66. Can a coefficient of determination be negative? Why or why not?
Page 684
Use the following information to answer the next exercise. The cost of a leading liquid laundry detergent in different sizes is given in Table
Size (ounces) Cost ($) Cost per ounce
16 3.99
32 4.99
64 5.99
200 10.99
82.
a. Using “size” as the independent variable and “cost” as the dependent variable, draw a scatter plot.
b. Does it appear from inspection that there is a relationship between the variables? Why or why not?
c. Calculate the least-squares line. Put the equation in the form of: ŷ=a+bx
d. Find the correlation coefficient. Is it significant?
e. If the laundry detergent were sold in a 40-ounce size, find the estimated cost.
f. If the laundry detergent were sold in a 90-ounce size, find the estimated cost.
g. Does it appear that a line is the best way to fit the data? Why or why not?
h. Are there any outliers in the given data?
i. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would you cost? Why or why not?
j. What is the slope of the least-squares (best-fit) line? Interpret the slope.
1 Improving the productivity of chickens. Farmers have discovered that more domestic chickens peck at objects placed in their environment, the healthier and more productive the chickens seem to be. White string has been found to be a particularly attractive pecking stimulus. In one experiment, 72 chickens were exposed to be a sting stimulus. Instead white sting, blue-colored string was used. The number of pecks each chicken took at the blue string over a specified time interval was recorded. Summary statistics for the 72 chickens were x̅=1.13 pecks, s= 2.21 pecks (Applied Animal Behavior Science, Oct. 2008).
Previous research has shown that μ=7.5 pecks if chickens are exposed to white string. Conduct a test (at α=.01) to determine if the true mean number of pecks at blue string is less than μ=7.5 pecks.
(a) Formulate the null and the alternative hypothesis.
(b)State and calculate the test statistics from the data.
(c) Draw a conclusion.
2. A five-year-old census recorded that 20% of the families in a large community lived below the poverty level. To determine if this percentage has changed, a random sample of 400 families is studied and 70 are found to be living below the poverty level. Does this finding indicate that the current percentage of families earning incomes below the poverty level has changed from what it was five years ago? Test with α=0.05.
(a) Formulate the null and the alternative hypothesis.
(b) State and calculate the test statistics from the data.
(c) Draw a conclusion.
(d) Calculate the P-value.
3. A city health department wishes to determine if the mean bacteria count per unit volume of water at a lake beach is within the safety level of 200. A researcher collected 10 water samples of unit volume and found the bacteria counts to be
175, 190, 205, 193, 184, 207, 204, 193, 196, 180
Do the data strongly indicate that there is no cause for concern? Test with α=0.05.
(a) Formulate the null and the alternative hypothesis.
(b) State and calculate the test statistics from the data.
(c)Draw a conclusion.
(d) Calculate the P-value.
4. A limnologist wishes to estimate the mean phosphate content per unit volume of the lake water. It is known from studies in previous years that the standard deviation has a fairly stable value of σ=4. How many water samples must the limnologist analyze to be 90% certain that the error of estimation does not exceed 0.8 milligrams?
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