Question

Length of a rod: Engineers on the Bay Bridge are measuring tower rods to find out if any rods have been corroded from salt water. There are rods on the east and west sides of the bridge span. One engineer plans to measure the length of an eastern rod 25 times and then calculate the average of the 25 measurements to estimate the true length of the eastern rod. A different engineer plans to measure the length of a western rod 20 times and then calculate the average of the 20 measurements to estimate the true length of the western rod. Suppose the engineer who collected 25 measurements for the eastern rod has a mean length of 23.9 feet with a standard deviation of 0.5 feet. The critical T-value for a 90% (one-sample) confidence interval with df = 24 is T=1.71. Which of the following is the resulting 90% confidence interval? Group of answer choices (23.73 , 24.07) (23.05, 24.76) (23.80, 24.00)

Answer 1

The 90% confidence interval for population mean length of eastern rods is (23.73, 24.07).

Explanation:

The (1 - α)% confidence interval for population mean when the population standard deviation is not known is:

`CI=\bar x\pm t_(\alpha/2, (n-1))\ (s)/(√(n))`

The information provided is:

`n=25\\\bar x=23.9\ \text{feet}\\s=0.50\ \text{feet}\\t_(\alpha/2, (n-1))=t_(0.05, 24)=1.71\\`

Compute the 90% confidence interval for population mean length of eastern rods as follows:

`CI=\bar x\pm t_(\alpha/2, (n-1))\ (s)/(√(n))`

`=23.9\pm 1.71*(0.50)/(√(25))\\\\=23.9\pm 0.171\\\\=(23.729, 24.071)\\\\\approx (23.73, 24.07)`

Thus, the 90% confidence interval for population mean length of eastern rods is (23.73, 24.07).