Spring 2015Math 227Test 4Name: ______

Show your work clearly, neatly, systematically and understandably. Round the decimal for probability to 5-decimal place and round the percentage to 3-decimal. Use proper notation.

1.(23:6,8,9)Suppose that against a certain opponent the number of points the MIT basketball team scores is normally distributed with unknown mean  and unknown variance, σ2. Suppose that over the course of the last 10 games between the two teams MIT scored the following points:

59, 62, 59, 74, 70, 61, 62, 66, 62, 75

  1. Find the sample mean and sample standard deviation.
  1. Compute a 95%–CI for.
  1. Compute a 95%–CI for σ.

2.(10:3,3,4) Find the critical values.

  1. Assume that the normal distribution applies. Find the critical value.

Right-tailed test; .

  1. Assume that t-distribution applies. Find the critical value.

Left-tailed test; , and n = 19.

  1. Assume that the chi-square distribution applies. Find the critical values.

Two-tailed test; , n = 16.

3.(7)The volume in a set of wine bottles is known to follow a N(µ, 25)-distribution. You take a sample of the bottles and measure their volumes. How many bottles do you have to sample to have a 96% confidence interval for µ with width 1? Note: The width of the CI is twice the margin-of-error.

4.(12:7,5) You do a poll to see what population proportion p supports candidate A over candidate B.

  1. How many people do you need to poll to know p to within 1% with 97% CL.
  1. (Hard!) Let p be the population proportion who prefer candidate A. If you poll 400 people, how many have to prefer candidate A to so that the 90% confidence interval is entirely above p = 0.5. Hint: You need to solve for x: , use in E.

5.(8)A mileage test is conducted for a new car model, the “Greenie.” Thirty randomly selected Greenies are driven for a month and the mileage is carefully measured in each. The sample mean mileage is 28.6 mpg and the sample standard deviation is 2.2 mpg. Test the claim that the average mpg for all Greenies is at least 27 mpg. Use  = 0.02.

6.(8)A recent USA TODAY/CNN/Gallup Poll showed that most American people support Bush’s efforts in the Middle East peace process. The poll of 2000 adults was conducted and 1243 people said they supported Bush’s efforts. Was Bush's efforts supported by more than 60% of the population?

7.(8)Last year the government made a claim that the average income of the American people was $43,950.However, a sample of 50 people taken recently showed an average income of $44,076 with a population standard deviation of $324.Conduct a significance test to see if the true mean is more than the reported average.Use =0.01.

8.(8)A company produces metal pipes of a standard length, and claims that the standard deviation of the length is at most 1.2 cm. One of its clients decides to test this claim by taking a sample of 25 pipes and checking their lengths. They found that the standard deviation of the sample is 1.5 cm. Does this undermine the company’s claim?

9.(8)STOCK INVESTMENT RISK: One measure of the risk of an investment stock is the standard deviation of its daily stock price. Vince McMahon, Chairman and CEO of World Wrestling Entertainment, Inc, claims that his company’s stock WWE qualifies as having moderate risk (i.e., if the standard deviation of its daily share price is less than $4). A stock market rating agency does not believe this claim and randomly selects 27 daily share prices, taken over the previous year. The sample standard deviation of these 27 daily share prices is computed to be $5.16. Conduct the appropriate test of hypothesis to determine if the agency’s conjecture is correct. Use .

10.(13:5,8)Tennis Racket String Tension:A local tennis pro-shop strings tennis rackets at the tension (pounds per square inch, or psi) requested by the customer. Emily, an avid tennis player from Redondo Beach, suspects that the pro-shop consistently strings rackets at lower tensions, on average, than requested. To support her claim, Emily asked the pro shop to string 13 new rackets at 65 psi. Following are the 13 tensions, that Emily was able to confirm independently: 53, 66, 62, 65, 59, 60, 61, 67,64, 64, 63, 65, 62

Does this sample data support Emily’s claim? Use . Note: You need to find sample mean and sample standard deviation first.