1. A company produces cans of stewed tomatoes with an advertised weight of 14 ounces.The company's quality-control engineer wants to check whether the cans actually do average 14 oz.For her test she randomly selects 35 cans and obtains an average of 13.9 oz and standard deviation of 0.34 oz.

At a significance level of = 0.05, does the data give convincing evidence that the average weight of the cans is less than 14 ounces?

2.Nationally, the proportion of red cars on the road is 0.12. A statistically-minded fan of the Philadelphia Phillies (whose team color is red) wonders if Phillies fans are more likely to drive red cars. One day during a home game, he takes an SRS of 210 cars parked at Citizens Bank Park (the Phillies home field) while a game is being played, and counts 35 red cars. Is this convincing evidence that Phillies fans prefer red cars more than the general population?

Support you conclusion with a test of significance.

3. Lumber companies dry freshly-cut wood in kilns before selling it.As a result of the drying process a certain percentage of the boards crack and become unusable.The current drying procedure for red oak boards is known to produce cracks in 16% of the boards.The drying supervisor at a lumber company wants to test a new method to determine if fewer boards crack.Suppose the drying supervisor uses the new method on an SRS of boards and finds that the sample proportion of checked boards is 0.11, which produces a p-value of 0.027.If the supervisor is convinced the new treatment is better, then they will spend money to install new equipment so they can use the new treatment on all of their lumber.

(a)Define the parameter of interest and write the appropriate null and alternative hypotheses for the test that is described.

(b)What conclusion would you draw at the = 0.05 level?

(c)Describe a Type I and a Type II error in this situation and the consequences of each.

Type I:

Type II:

(d)The supervisor is considering changing the significance level of the test to 1%.Discuss the impact this might have on the Type I and Type II error probabilities and the power of the test. (don't have to calculate any numbers, just say if each would increase, decrease, or stay the same)