1.) Suppose the 90% confidence interval for the mean SAT scores of applicants at a business college is given by [1,695, 1,836]. This confidence interval uses the sample mean and the sample standard deviation based on 25 observations.[You may find it useful to reference thet table.]What are the sample mean and the sample standard deviation used when computing the interval?(Round “t” value to 3 decimal places and “Sample mean” and “Sample standard deviation” to 2 decimal places.)Sample meanSample standard deviation2.) A sample of 105 results in 63 successes.[You may find it useful to reference thez table.]a.Calculate the point estimate for the population proportion of successes.(Do not round intermediate calculations. Round your answer to 3 decimal places.)point estimateb.Construct 95% and 90% confidence intervals for the population proportion.(Round intermediate calculations to at least 4 decimal places. Round “z” value and final answers to 3 decimal places.)Confidence interval95% to90% toc.Can we conclude at 95% confidence that the population proportion differs from 0.680?multiple choice 1No, since the confidence interval does not contain the value 0.680.No, since the confidence interval contains the value 0.680.Yes, since the confidence interval does not contain the value 0.680.Yes, since the confidence interval contains the value 0.680.d.Can we conclude at 90% confidence that the population proportion differs from 0.680?multiple choice 2Yes, since the confidence interval does not contain the value 0.680.Yes, since the confidence interval contains the value 0.680.No, since the confidence interval does not contain the value 0.680.No, since the confidence interval contains the value 0.680.3.) You need to compute the a 95% confidence interval for the population mean. How large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 1.0? (Use 5.0 as an estimate of the population standard deviation from prior studies.)(You may find it useful to reference thez table. Round intermediate calculations to at least 4 decimal places. Round “z” value to 3 decimal places. Round up your answer to the nearest whole number.)Sample Size4.) Subprime lending was big business in the United States in the mid-2000s, when lenders provided mortgages to people with poor credit. However, subsequent increases in interest rates coupled with a drop in home values necessitated many borrowers to default. Suppose a recent report finds that two in five subprime mortgages are likely to default nationally. A research economist is interested in estimating default rates in Illinois with 99% confidence.[You may find it useful to reference thez table.]How large a sample is needed to restrict the margin of error to within 0.07, using the reported national default rate?(Round “z” value to 3 decimal places. Do not round intermediate calculations. Round up your final answer to nearest whole number.)Sample sizeMathStatistics and Probability QUAN 202
