Number 12 There are 614,387 bridges in the United States. A senator sponsors a b

Question

Number 12

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. 2. Construct a 99% confidence interval for the population proportion 3. Test the claim at = 0.01 4. 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. 15 16 17 17 19 22 25 26 26 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 5. Given this sample, create a frequency distribution using 8 classes. Draw a frequenc 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 years. Construct 11. If = 21.5 years, how large a sample would be required to be 95% confident that the true 12. Test the claim that the average bridge is more than 40 years old, at -0.05 with 21.5 11 Cnndian novernment study finds that in a sample of 20 Canadian bridges, the average a 95% confidence interval for the population mean mean is within 2 years of the sample mean years intion of 15.5 years. Can you conclude

Explanation / Answer

Question 12

H0 : < = 40 years

Ha : > 40 years

Here standard deviation = 21.5 years

standard error of sample mean se0 = / sqrt(n) = 21.5/ sqrt(50) = 3.04056

Here test statistic

Z = (x - H)/ se0 = (45.32 - 40)/3.04056 = 1.75

as test is one tailed

P - value = Pr(Z > 1.75) = 0.04

so as p - value is less than alpha level = 0.05 so we shall reject the null hypothesis and can conclude that the average bridge is more than 40 years old.

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