1) Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x of a 1-year old baby and the weight yof the mature adult (30 years old)? A random sample of medical files produced the following information for 14 females: Complete parts (a) through (c), given x = 302, y = 1771, x2 = 6664, y2 = 225,135, and xy = 38,378. (a) Find x, y, and b. (Round your answers for x and y to two decimal places. Round your answer for b to four decimal places.) x= y= b= b) Find the equation of the least-squares line. (Round your answers to four decimal places.) = + x (c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.) r = r2 = d) What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) % (e) If a female baby weighs 16 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) lb Suppose you took random samples from three distinct age groups. Through a survey, you determined how many respondents from each age group preferred to get news from T.V., newspapers, the Internet, or another source (respondents could select only one mode). What type of test would be appropriate to determine if there is sufficient statistical evidence to claim that the proportions of each age group preferring the different modes of obtaining news are not the same? Select from tests of independence, homogeneity, goodness-of-fit, and ANOVA. Since we are determining if the current distribution of fits the previous distribution of responses, the goodness-of-fit test is appropriate. 2) Since we are comparing three distinct age groups, the test of two-way ANOVA is appropriate. Since we are interested in proportions, the test for homogeneity is appropriate. Since we can claim all the variables are independent, the test of independence is appropriate. Since we are comparing to a fixed variance, the test of ANOVA is appropriate. Professor Stone complains that student teacher ratings depend on the grade the student receives. In other words, according to Professor Stone, a teacher who gives good grades gets good ratings, and a teacher who gives bad grades gets bad ratings. To test this claim, the Student Assembly took a random sample of 300 teacher ratings on which the student's grade for the course also was indicated. The results are given in the following table. Test the hypothesis that teacher ratings and student grades are independent at the 0.01 level of significance. Rating A B C F (or withdrawal) Row Total Excellent 10 17 12 5 44 Average 25 31 73 14 143 Poor 21 28 44 20 113 Column Total 56 76 129 39 300 3) (a) Give the value of the level of significance. (b) State the null and alternate hypotheses. H0: Student grade and teacher rating are independent. H1: Student grade and teacher rating are not independent. H0: The distributions for the different ratings are the same. H1: The distributions for the different ratings are different. H0: Tests A, B, C, F (or withdrawal) are independent. H1: Tests A, B, C, F (or withdrawal) are not independent. H0: Ratings of excellent, average, and poor are independent. H1: Ratings of excellent, average, and poor are not independent. (c) Find the sample test statistic. (Round your answer to two decimal places.) d) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) e) Conclude the test. Since P-value , we reject the null hypothesis. Since P-value < , we reject the null hypothesis. Since P-value , we do not reject the null hypothesis. Since P-value < , we do not reject the null hypothesis. 4) A sociologist is studying the age of the population in Blue Valley. Ten years ago, the population was such that 21% were under 20 years old, 11% were in the 20- to 35-year-old bracket, 33% were between 36 and 50, 24% were between 51 and 65, and 11% were over 65. A study done this year used a random sample of 210 residents. This sample is given below. At the 0.01 level of significance, has the age distribution of the population of Blue Valley changed? Under 20 20 - 35 36 - 50 29 25 68 a) Give the value of the level of significance. 51 - 65 Over 65 67 21 b) State the null and alternate hypotheses. (Please highlight the correct answer). H0: The population 10 years ago and the population today are independent. H1: The population 10 years ago and the population today are not independent. H0: Ages under 20 years old, 20- to 35-year-old, between 36 and 50, between 51 and 65, and over 65 are independent. H1: Ages under 20 years old, 20- to 35-year-old, between 36 and 50, between 51 and 65, and over 65 are not independent. H0: The distributions for the population 10 years ago and the population today are the same. H1: The distributions for the population 10 years ago and the population today are different. H0: Time ten years ago and today are independent. H1: Time ten years ago and today are not independent. c) Find the sample test statistic. (Round your answer to two decimal places.) d) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) e) Conclude the test. Since P-value < , we reject the null hypothesis. Since P-value , we do not reject the null hypothesis. Since P-value , we reject the null hypothesis. Since P-value < , we do not reject the null hypothesis