Does the maker of M&MS (Mars, Inc.) use the same proportion of red candies in its plain and peanut varieties? A random sample of 57 plain M&Ms contained 11 red candies, and another random sample of 35 peanut M&Ms contained 9 red candies. (Use p1 for the proportion of red candies in plain M&Ms and J32 for the proportion of red candies in peanut M&Ms.) (a) Construct a 95% confidence interval for the difference in the proportions of red candies for the plain and peanut varieties (pl 7 p2). (Round your answers to three decimal places.) :lto: (b) Based on the confidence interval in part (a), can you conclude that there is a difference in the proportions of red candies for the plain and peanut varieties? Explain. 0 Since the value pl 7 p2 = 0 is not in the confidence interval, it is possible that [.31 = p2. We should conclude that there is a difference in the proportion of red candies in plain and peanut M&Ms. 0 Since the value pl 7 p2 = 0 is in the confidence interval, it is p055ible thatp1 = 02' We should not conclude that there is a difference in the proportion of red candies in plain and peanut M&Ms. 0 Since the value p1 p2 : D is in the confidence interval, it is posSible thatp1 : p2 We should conclude that there is a difference in the proportion of red candies in plain and peanut M&Ms. 0 Since the value p1 p2 : O is not in the confidence interval, it is possible that p1 : p2. We should not conclude that there is a difference in the proportion of red candies in plain and peanut M&Ms In a study of the relationship between birth order and university success, an investigator found that 122 in a sample of 180 university graduates were firstborn or only children. In a sample of 100 non-graduates of comparable age and socioeconomic background, the number of firstborn or only children was 52. Estimate the difference between the proportions of firstborn or only children in the two populations from which these samples were drawn (P, - p2). Use a 90% confidence interval. (Use p, and P2 for the proportions of firstborn or only children who were university graduates and non-graduates, respectively. Round your answers to three decimal places.) to Interpret your results. O There is a 90% chance that a single difference in sample proportions will fall within the interval. O In repeated sampling, 90% of all intervals constructed in this manner will enclose the true value of P1 - P2. 0 90% of all proportions will fall within the interval. There is a 10% chance that a single difference in sample proportions will fall within the interval. O In repeated sampling, 10% of all intervals constructed in this manner will enclose the true value of P1 - P2.Last year's records of auto accidents occurring on a given section of highway were classified according to whether the resulting damage was $1,000 or more and to whether a physical injury resulted from the accident. The data follows. Under $1,000 $1,000 or More Number of Accidents 37 44 Number Involving Injuries 8 24 (a) Estimate the true proportion of accidents involving injuries when the damage was $1,000 or more for similar sections of highway. (Round your answer to three decimal places.) Find the 95% margin of error. (Round your answer to three decimal places.) (b) Estimate the true difference in the proportion of accidents involving injuries for accidents with damage under $1,000 and those with damage of $1,000 or more. Use a 95% confidence interval. (Use P1 - P2 where p, is the proportion of accidents involving injuries with damage under $1,000 and p2 is the proportion of accidents involving injuries with damage of $1,000 or more. Round your answers to three decimal places.) to You may need to use the appropriate appendix table or technology to answer this question.Find a 90% one-sided upper confidence bound for the population mean ,u for these values. (Round your answers to two decimal places.) (a) n=38, 52:68, x=70 S (b) n= 100, 5: 2.1, X: 1.5 Z You may need to use the appropriate appendix table or technology to answer this