Number 13 There are 614,387 bridges in the United States. A senator sponsors a b
ID: 3325488 • Letter: N
Question
Number 13
There are 614,387 bridges in the United States. A senator sponsors a bill to raise taxes to pay for repairs to those bridges. To support her bill, she claims that more than 5% of bridges in theUnited States are structurally deficient, and the average bridge in the United States is more than 40 years old. To support that claim, she initiates a study of the nation's bridges through the U.S. Army Corps of Engineers to test 200 bridges to see if each bridge is structurally deficient. 1. Describe how to collect a random sample of 200 bridges from this population Construction engineers from the Army Corps of Engineers conduct the study of the nation's bridges. Of the 200 bridges tested, 15 are deemed structurally deficient. Construct a 99% confidence interval for the population proportion 2. 3. Test the claim at = 0.01 How large a sample would be required to be 99% confident that the true proportion is within 1% of the sample proportion? The ages of 50 bridges are shown below 6 26 29 32 33 35 35 36 39 39 42 44 46 46 47 48 49 50 51 52 52 54 57 59 60 62 62 63 65 67 69 72 74 83 85 92 96 103 15 16 17 17 19 22 25 26 26 5. Given this sample, create a frequency distribution using 8 classes. Draw a frequency histogram 6. Find the mean, median, mode, range, variance, and standard deviation of the sample 7. Construct a boxplot representing the sample. 8. Construct a 95% confidence interval for the population mean. 9. Test the claim that the average bridge is more than 40 years old, at = 0.05 10. Suppose that we know the population standard deviation is actually 21.5 year s. Construct a 95% confidence interval for the population mean 11. If = 21.5 year s, how large a sample would be required to be 95% confident that the true mean is within 2 years of the sample mean Test the claim that the average bridge is more than 40 years old, at -0.05 w years th = 21 .5 a sample of 20 Canadian bridges, the average years. Can you conclude 13. A Canadian government study finds that in bridge is 38 years old, with a sample standard deviation of 15.5 hat the averag bridge, at e age of a Canadian bridge is different than the average age of an American 0.05? Use the sample standard deviation found in question 6Explanation / Answer
H0 : u = 40
H1 : u 40
Decision rule : If T statistic < -2.093 or > 2.093 then reject H0
T statistic = xbar - µ /(/n)
= 38 - 40 / [15.5/(20)] = -0.577
Here T statistic > -0.577 So fail to reject H0
we conclude that there is no sufficient evidence that andian mean is different than american mean
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