Fundamentals of Statistics

1.A nearby school is trying a new format for teaching reading to elementary school students. The following hypotheses are tested.

 

H0: The new format does not improve reading ability.

Ha: The new format does improve reading ability. 

 

What is the Type I error for these hypotheses? 


2.For the hypotheses above: What is at least one consequence of a Type I Error?


3.For the hypotheses above: What is the Type II error for these hypotheses?


4.Consumer Reports has stated that the mean time for a Chrysler Concorde to accelerate from 0 mph to 60 mph is 8.7 seconds. Is the time longer at higher altitudes?  Perform a complete hypothesis test to see.  Assume that a sample of 15 trials in a city with elevation if 10,000 feet above sea level, the average time was 9.2 seconds.  Assume  LaTeX: \sigmaσ= 6.5 seconds.  Let LaTeX: \alphaα = 0.05.


5.The price-to-earnings (P/E) ratio is important in financial work. It is the ratio of the company’s share price to their earning per share.   A random sample of 14 large banks had an average P/E of 17.1 with a standard deviation of 4.7.  Typically, lower P/E ratios are better for new investments.  If a recent average P/E for all of the S&P 500 stocks was 19, perform a complete hypothesis test to see if the large banks have a lower average P/E then all S&P 500 stocks.  Let the level of significance be 0.10.



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