Lane Chap. 142. 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?6. For the X, Y data below, compute: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.X435111014Y671217921Lane Chap. 175. At a school pep rally, a group of sophomore students organized a free rafﬂe for prizes. Theyclaim that they put the names of all of the students in the school in the basket and that theyrandomly drew 36 names out of this basket. Of the prize winners, 6 were freshmen, 14 weresophomores, 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 distributedthroughout the classes as would be expected based on the percentage of students in eachgroup. Report your Chi Square and p values.c. What do you conclude?14. A geologist collects hand-specimen sized pieces of limestone from a particular area. Aqualitative assessment of both texture and color is made with the following results. Is thereevidence of association between color and texture for these limestones? Explain your answer.COLOUR TextureFineMediumCoarseLight4521Medium202323Dark8124Illowsky Chap.11Decide whether the following statements are true or false.70. The standard deviation of the chi-square distribution is twice the mean.Use the following information to answer the next exercise: Suppose an airline claims that itsflights are consistently on time with an average delay of at most 15 minutes. It claims that theaverage delay is so consistent that the variance is no more than 150 minutes. Doubting theconsistency 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= ________Illowsky Chap.1266. Can a coefficient of determination be negative? Why or why not?The cost of a leading liquid laundry detergent in different sizes is given.Size (Ounces)163264200Cost ($)3.994.995.9910.99Cost per ounces82.a. Using “size” as the independent variable and “cost” as the dependent variable, draw a scatterplot.b. Does it appear from inspection that there is a relationship between the variables? Why or whynot?c. Calculate the least-squares line. Put the equation in the form of: ŷ=a+bxd. 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 detergentwould you cost? Why or why not?j. What is the slope of the least-squares (best-fit) line? Interpret the slope.