Q-1 In a population, µY = 100 and σ 2 Y = 43. Use the central limit theorem to answer the following: a. In a random sample of size n = 100, find P r (Y < 101). b. In a random sample of size n = 64, find P r (101 < Y < 103). c. In a random sample of size n = 165, find P r (Y > 98).
Q-2 Suppose CUNY professors have an average life, normally distributed, of ?? = 80 years with a population standard deviation of 9 years. a. What percent of CUNY professors will live more than 96 years? b. What percent of CUNY professors will not make it past the age of 60? c. Calculate the 96th percentile. d. Calculate the 2nd percentile. e. What proportion of CUNY professors will live between 70 and 85 years?
Q-3 The average hourly wage of plumbers is normally distributed with a population mean of $24.00 and a population standard deviation of $6.00. Calculate the following: a. The proportion of plumbers earning between $18 and $22 b. The proportion of plumbers earning more than $28 c. The proportion of plumbers earning less than $15 d. The 70th percentile
Q-4 A drug company that manufactures a diet drug claims that those using the drug for 30 days will lose at least 15 pounds. You sample 30 people who have used the drug and find that the average weight loss was 12 pounds with a standard deviation of 5 pounds. (Hint : When sample is small enough i.e. η ≤ 30 use a t-test) a. Test the claim at the .05 significance level. b. No claim was made by the company. They took a sample with the above results and ask you to construct a two-sided 95% confidence interval for the population mean.
Q-5 Suppose the population standard deviation σ is 40 based upon previous studies. We would like to estimate the population mean within ±8 of its true value, at a significance level of .05 (95% Confidence interval). What sample size should be taken?
Q-6 A manufacturer produces drill bits with an intended life of at least 580 hours and a standard deviation of 30 hours. A quality control scientist draws a sample of 100 bits and finds X = 577. Test at α = .05 to see if the machinery needs adjusting.
Q-7 An LSAT preparation school claims that its review course will add at least 50 points to the score of a student retaking the LSAT exam. You sample 25 students and find that average improvement was 40 points with a standard deviation of 15 points 1 a. Test the claim at the .05 significance level b. No claim was made by the school. They took a sample with the above results and ask you to construct a two-sided 95% confidence interval for the population mean.
Q-8 A company claims that cancer patients using drug X will live at least 10 more years. n=16, X = 8.8 year, s = 3.4 year. Test the claim made by the company at 1%,5%, and 10% significance level.
Q-9 A company claims that its soup machines deliver exactly 10.0 ounces of soup-no more, no less. A researcher samples 100 bowls of soup and finds that: ??= 10.28 ounces s = 1.20 ounces Test the company's claim at 5% and 1% significance level.
Q-10 The state of Alabama wants to know the lower limit of a two-sided 90% confidence interval for reading scores of graduating seniors at all high schools in Alabama. They sampled 900 students and found that the sample mean was 11.30 and the sample standard deviation was 1.50.