1. 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?
2. For the (X,Y) data points below, compute:
Data Points: (4,6), (3,7), (5,12), (11,17), (10,9), (14,21)
a. The correlation (r) and determine if it is significantly different from a hypothesized slope of 0 (null hypothesis). HINT: Use the significance test for correlation on Page-482 and assume a 95% confidence.
b. The slope and intercept of the linear regression line
3. At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. The results do not seem that random to you. You think it is a little fishy that sophomores organized the raffle and also won the most prizes. Your school is composed 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 prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. Report your Chi Square and p values.
c. What do you conclude about the null hypothesis (the observed and expected data are the same) assuming a 95% confidence?
4. A geologist collects hand-specimen sized pieces of limestone from a particular area. A qualitative assessment of both texture and color is made with the following results. Is there evidence of association between color and texture for these limestones? Explain your answer by testing your null hypothesis assuming a 95% confidence level.
70. TRUE or FALSE ... The standard deviation of the chi-square distribution is twice the mean.
5. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in the table. Conduct a test for homogeneity at a 5% level of significance (?=0.05).
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. Find df
117. Let =0.05. What is your decision regarding the hypothesis? Write your conclusion in a sentence and discuss whether there is sufficient data to support your decision. HINT: See Section 11.6 on "Test of a Single Variance".
66. Can a coefficient of determination be negative? Why or why not?
82. The cost of a leading liquid laundry detergent in different sizes is given in the table.
a. Using "size" as the independent variable (x) and "cost" as the dependent variable (y), and draw a scatter plot using EXCEL.
b. Calculate the least-squares line. Put the equation in the form of: y = a + bx. See the instructors "EXCEL Tips" for finding a linear regression.
c. Find the correlation coefficient. Is it significant?
d. If the laundry detergent were sold in a 40-ounce size, find the estimated cost.
e. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would you cost? Why or why not?
f. What is the slope of the least-squares (best-fit) line? Interpret the slope.
(1) TRUE or FALSE. Explain your answer for full credit. (2 points each, 10 points total)
(a) In a normal distribution, 68% of the area under the curve is within one standard deviation of the mean. (b) Given that a normal distribution has a mean of 50 and standard deviation of 5. The median is also 50. (c) If the variance from a set of data is zero, then all of the data values must be identical.?(d) A 95% confidence interval is wider than and 99% confidence interval of the same parameter.
(e) It is easier to reject the null hypothesis if we a smaller significance level (α).
(2) The patient recovery time from a surgical procedure is normally distributed with a mean of
5.3 days and standard deviation of 2.1 days. (5 points each, 10 points total)
(a) What is the probability of spending more than 2 days in recovery after a surgical procedure? (b) What is the 90th percentile for recovery time after a surgical procedure?
(3) Human heights are known to be normally distributed. Men have a mean height of 70 inches and females a mean height of 64 inches. Both have a standard deviation of 3 inches.?(3 points each, 15 points total)
(a) Find the 1st Quartile (Q1) of the female height distribution?(b) Find the height of a female in the 90th percentile?(c) What is the probability that a randomly selected female is above 70 inches height?
Assume a random sample of 100 males is selected.
(d) What is the standard deviation of the sample mean??(e) What is the probability that the mean height of samples is less than 68 inches tall
(4) The average height of students has a normal distribution with a standard deviation of 2.5 inches. You want to estimate the mean height of students at your college to within 1-inch with 95% confidence. How many students should you measure? HINT: Be sure to consider the two-tail probability when evaluating the z-score for the confidence level. (10 points)
(5) A random sample of 150 test scores has a sample mean of 80. Assume that the test scores have a population standard deviation of 15. Construct a 95% confidence interval estimate of the mean test scores. (10 points)
(6) A statistics instructor believes that 50% of his students are male. One of his students thinks there are more males than females taking statistics, so he decides to conduct a random survey of past courses. He found that 83 of 150 students were male. Answer the questions below. HINT: This is a test of a single population proportion. See Example 9.17 on page 487 of the textbook.
(3 points each, 15 points total)
(a) What is the null hypothesis (Ho) and what is the alternate hypothesis (Ha)??(b) What is the standard error of the proportion??(c) What is the test statistic??(d) What is the P-value for this test? HINT: Assume a normal distribution and use the single population proportion equations on page-502 of Illowsky.
(e) Is there sufficient evidence to reject the null hypothesis (Ho) at a 99% confidence level (α=0.01)?
(7) Taking an SAT preparatory course is believed to improve test scores. To investigate the effects of taking a preparatory course, scores were recorded for 5 students before and and after they took the preparatory course. Does the data below suggest that a preparatory course increases test scores? Assume we want a 90% confidence level (α=0.10) to test the claim. HINT: Assume the null hypothesis is that test scores stay the same, before and after taking the course. Also, assume the "expected" change in test scores is zero when evaluating the test statistic. (3 points each, 15 points total)
(a) Identify the alternate hypothesis?(b) What is the random variable (X) that we want to evaluate? (c) Find the test statistic (show all work)?(d) Find the P-value (show all work)?(e) Is there sufficient evidence to support the claim that taking a preparatory course increases an SAT test score? Justify your conclusion.
Student Before After
1 1200 1260
2 1150 1120
3 1260 1260
4 1050 1200
5 980 1050
(8) Researchers interviewed young adults in Canada and the U.S to compare their ages when they enter the workforce. The mean age of the 100 Canadians was 18 with a standard deviation of 6. The mean age of the 130 people interviewed in the U.S. was 20 with a standard deviation of 8. Is the mean age of entering the workforce in Canada lower than the mean age in the U.S.? (5 points each, 15 points total)
(a) Identify the null and alternate hypothesis?(b) Find the test statistic (show all work). HINT: You are testing two population means with known standard deviations. See the equation on page-554.?(c) Find the P-value (show all work) and evaluate whether the mean age of entering the workforce in Canada is lower than the mean age in the U.S.? Test at a 1% significance level.