BRM Midterm 2 Questions With 100% Verified Solutions

BRM Midterm 2 Questions With 100% Verified Solutions In a survey of 3121 people, 412 are under-vaccinated. What is the proportion of under-vaccinated people in the local population? - ANSWER p̂ = x /n = 412/3121 = 0.132 Suppose you want to estimate the percentage of the time (with 95% confidence) you're expected to get a red light at a certain intersection. You take a random sample of 100 different trips through this intersection and you find that a red light was hit 53 times. - ANSWER p̂ = 53/100 = 0.53 0.53 - 1.96(√0.53*(1-0.53)/100) = 0.43 0.53 + 1.96(√0.53*(1-0.53)/100) = 0.63 In a recent poll of 200 households, 152 households had at least one computer, estimate the proportion of households in the population that have at least one computer. Construct a 95% interval to estimate population proportion. - ANSWER 0.76 - 1.96(√0.76(1-0.76)÷200) = 0.701 0.76 + 1.96(√0.76(1-0.76)÷200) = 0.819 In words, we are 95% confident that the proportion of households in the population with at least one computer is between 0.701 to 0.819 Suppose that a market research firm is hired to estimate the percent of adults living in a large city who have cell phones. Five hundred randomly selected adult residents in this city are surveyed to determine whether they have cell phones. Of the 500 people surveyed, 421 responded yes - they own cell phones. Using a 95% confidence level, compute a confidence interval estimate for the true proportion of adult residents of this city who have cell phones. - ANSWER 0.842 - 1.96(√0.84(1-0.84)÷500) = 0.815 0.842 + 1.96(√0.84(1-0.84)÷500) = 0.869 (0.815, 0.869) 800 randomly selected college students at university XYZ were asked if they own a laptop. 584 responded yes to the survey. Construct a 95% confidence interval to estimate the true population proportion of students at university XYZ who own laptops and determine the margin of error. - ANSWER E = 1.96(√0.73(1-0.73)÷800) = 0.0308 800 randomly selected college students at university XYZ were asked if they own a laptop. 584 responded yes to the survey. What sample size is needed to estimate the true population with a 2% margin of error at 90% confidence level. - ANSWER n = (1.645)^2 (0.73) (0.27) / (0.02)^2 n = 1334 A company manufactures calculators with an average mass of 450g. An engineer believes the average weight to be different. He decides to calculate the average mass of 50 calculators. State the null and alternative hypothesis. - ANSWER H0 : μ = 450 Ha : μ != 450 A teacher in a school believes that at least 70% students will complete high school. A student disagrees and decides to conduct a test. State the null and alternative hypothesis. - ANSWER H0 : P = 0.70 Ha : P 0.70 A teacher wishes to test if the average GPA of students in the high school is different than 2.7. State the null hypothesis and Alternative hypothesis - ANSWER H0 : μ = 2.7 Ha : μ != 2.7 The percentage of residents who own a car in a town is no more than 75%. A researchers disagrees with the value and decides to survey 100 residents asking them if they own a car. State the null hypothesis and alternative hypothesis. - ANSWER H0 : P = 0.75 Ha : P 0.75 A government official claims that the dropout rate for local schools is 25%. Last year, 190 out of 603 students dropped out. Is there enough evidence to reject the government official's claim? - ANSWER Drop out rate = 25% two tails test A government official claims that the dropout rate for local schools is less than 25%. Last year, 190 out of 603 students dropped out. Is there enough evidence to reject the government official's claim? - ANSWER Drop out rate 25%