Researchers at a metals lab are testing a new alloy for use in high end electron

Question

Researchers at a metals lab are testing a new alloy for use in high end electronics. The alloy is very expensive to make so their budget for testing is limited. The researchers need to estimate the average force required to bend a piece of the alloy to a 90 degree angle. From previous tests, the standard deviation is known to be 22.714 Newtons. In order to estimate the true mean within a margin of error of 6.87 Newtons with 90% confidence, how many samples would need to be tested?

Question 1 options:

Suppose that you are the director of table game operations at a large casino, known especially for its poker room. You are interested in determining the average number of hands the casino should expect per hour during peak hours in the poker room. You monitor the number of hands over the next week and given a random sample of 29 hours, you see that on average 162.87 hands are played per hour, with a standard deviation of 9.687 hands and you calculated a 99% confidence interval to be (157.899, 167.841). Your manager believes the true mean is 162.7. Which of the following is the best conclusion?

Question 3 options:

You are curious about the average number of yards Matthew Stafford throws for each game for the Detroit Lions. You randomly select 22 games and see that the average yards per game is 273.2 with a standard deviation of 32.38 yards. You want to create a 99% confidence interval for the true average number of yards per game he throws. What is the margin of error for this estimate?

Question 4 options:

1) 29 2) We do not have enough information to answer this question since we were not given the sample mean. 3) 35 4) 30 5) 40

Explanation / Answer

1.

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.05  
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
s = sample standard deviation =    22.714  
E = margin of error =    6.87  
      
Thus,      
      
n =    29.57524033  
      
Rounding up,      
      
n =    30   [answer, OPTION 4]

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3.

As 162.7 is inside the interval (157.899, 167.841), then

OPTION 2: The average number of hands played per hour is not significantly different from 162.7 [ANSWER]

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