12. Do educational toys make a difference in age at which a child learns to read? Researchers designed an experiment in which a group of preschool twins was divided into a group who spent 2 hours each day in a room supplied with educational toys (Group A) and another group (Group B) who spent 2 hours each day in a room supplied with non-educational toys. The age in months when the child began reading a is recorded in the table below. Was there a difference between the two ages? Twin Pair 1 2 3 4 5 6 Group A 61 64 53 60 71 62 60 Group B 64 60 52 56 75 63 58 13. A private industry analyst claims that there is no difference in the salaries earned by workers in the manufacturing and construction industries. A random sample of 1 1 manufacturing and 11 construction workers and their salaries is shown in the table below. At a = 0.10, can you reject the analyst's claim? Assume underlying normal distributions. Industry Salary (in thousands of dollars) Manufacturing 31 38 33 45 35 43 33 29 38 41 32 Construction 31 30 27 32 28 34 30 33 26 35 28 14. You are a travel agent and wish to estimate the proportion of vacationers who plan to travel outside the United States within the next 12 months. Suppose that 50 vacationers are surveyed. It is found that 26% of these vacationers plan to travel outside the United States. Construct a 95% confidence interval for the population proportion of vacationers who plan to travel outside the LLS 15. Carbon dioxide-baited traps are typically used by entomologists to monitor mosquito populations. To determine whether temperature influences the number of mosquitoes caught in the trap, a researcher counted the number of mosquitoes caught on each of nine consecutive days. For each day two variables were measured: the temperature (degrees Centigrade) and the number of mosquitoes caught. Date 7/24 7/25 7/26 7/27 7/28 7/29 7/30 7/31 8/1 Temperature 16.8 15.0 16.5 17.7 20.6 22.6 23.3 18.2 18.6 # caught 66 30 46 44 67 99 75 24 51 a. Does the scatterplot relating the number of mosquitoes caught to the temperature indicate that you should proceed with a linear regression analysis? WHY? b. Find the equation for the regression line. c. Find the correlation coefficient. d. Find the coefficient of determination. e. Interpret and explain the relevancy or lack of relevancy of the y-intercept in terms of this problem. f. Interpret the slope in terms of this problem. g. Explain the meaning of the coefficient of determination in terms of this problem. h. If the temperature is 25 C, how many mosquitoes would you predict to be caught? i. If the temperature is 20C, how many mosquitoes would you predict to be caught
