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?6. 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 (nullhypothesis). HINT: Use the significance test for correlation on Page-482 and assume a 95% confidence.b. The slope and intercept of the linear regression line5. At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim thatthey put the names of all of the students in the school in the basket and that they randomly drew 36 namesout of this basket. Of the prize winners, 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 fishy that sophomoresorganized 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 throughoutthe classes as would be expected based on the percentage of students in each group. Report your ChiSquare and p values.c. What do you conclude about the null hypothesis (the observed and expected data are the same)assuming a 95% confidence?14. A geologist collects hand-specimen sized pieces of limestonefrom a particular area. A qualitative assessment of both texture andcolor is made with the following results. Is there evidence ofassociation between color and texture for these limestones? Explainyour 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.102. Do men and women select different breakfasts? The breakfasts ordered by randomly selected menand 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 15minutes. 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 next25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.113. Find df117. Let =0.05. What is your decision regarding the hypothesis? Write your conclusion in a sentenceand discuss whether there is sufficient data to support your decision. HINT: See Section 11.6 on “Test ofa Single Variance”.66.