A civil engineer plans to investigate 90 randomly selected sections of underground gas piping for minor...

A civil engineer plans to investigate 90 randomly selected sections of underground gas piping for minor cracks; these cracks could be of concern in the future. However, due to time constraints, the engineer could not inspect 22 of the initially selected pipes. Of those inspected, it is found that 12 possess minor cracks. Produce a 99% confidence interval for the proportion of pipes with minor cracks.

Expert Solution

Solution :

n = 90

x = 12

Point estimate = sample proportion = = x / n = 12/ 90 = 0.133

1 - = 1- 0.133 = 0.867

At 99% confidence level

= 1-0.99% =1-0.99 =0.01

/2 =0.01/ 2= 0.005

Z/2 = Z0.005 = 2.576

Z/2 = 2.576

Margin of error = E = Z / 2 * $\sqrt$ (( * (1 - )) / n)

= 2.576 * ( $\sqrt$ (0.133*(0.867) / 90)

= 0.092

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.133 -0.041 < p < 0.133 +0.041

0.041 < p < 0.226

( 0.041 , 0.226 )

orchestra answered 2 years ago

Vincent randomly selected a bag of M&Ms from a randomly selected gas station as he was...

Vincent randomly selected a bag of M&Ms from a randomly selected gas station as he was driving down the interstate. Being bored while riding in the car he decided to evaluate his green M&Ms. From the simple random sample there were 19 green M&Ms with a sample mean weight of 0.8635 g any sample standard deviation of 0.0570 g. Use a 0.05 significance level to test the claim that Janine week of all the M&Ms is equal to 0.8535

Suppose 90% of a sample of 100 randomly selected homes in Town A and 80% of...

Suppose 90% of a sample of 100 randomly selected homes in Town A and 80% of a sample of 50 randomly selected homes in Town B rely on the public water supply for drinking water. Compute the test statistic for a hypothesis test to compare the population proportion of homes that rely on the public water supply for drinking water in Town A to the proportion in Town B. Assume that the conditions for a hypothesis test for the difference...

Assume that the samples are independent and that they have been randomly selected. Construct a 90%...

Assume that the samples are independent and that they have been randomly selected. Construct a 90% confidence interval for the difference between population proportions p1-p2. Round to three decimal places. x1=12, n1=45 and x2=21, n2=51 A. -0.301 <p1-p2< 0.011 B. 0.453 <p1−p2 < 0.079 C. 0.109 <p1−p2< 0.425 D. 0.081 <p1−p2< 0.453

Of 150 patients randomly selected by a hospital, 90 of them said that their health insurance...

Of 150 patients randomly selected by a hospital, 90 of them said that their health insurance was not adequate. (a) Construct a 99% confidence interval for the proportion of patients who would say that their health insurance was not adequate. (b) Can we say that more than 50% of all patients of the hospital did not have adequate health insurance? Test at the 1% significance level.

In the survey on the quality of coffee A carried out among 90 randomly selected customers...

In the survey on the quality of coffee A carried out among 90 randomly selected customers of the company dealing with its distribution, the following ratings were obtained: Rating 1 2 3 4 5 6 7 8 9 Number of people 2 4 4 10 17 18 21 8 6 a) Based on the above data, the hypothesis was verified that 40% of all customers put coffee higher than '6' with the alternative that less than 40% giving such a...

A safety engineer records the braking distances of two types of tires. Each randomly selected sample...

A safety engineer records the braking distances of two types of tires. Each randomly selected sample has 35 tires. The results of the tests are shown in the table. At alpha equals 0.10, can the engineer support the claim that the mean braking distance is different for the two types of tires? Assume the samples are randomly selected and that the samples are independent. Complete parts (a) through (e). Type A 1x1 equals= 43feet 1σ1 equals= 4.7 feet Type B...

Suppose you randomly selected 40 gas stations in the Baton Rouge area and found that the...

Suppose you randomly selected 40 gas stations in the Baton Rouge area and found that the average price of regular unleaded gas is $3.04. Assume that population standard deviation is known to be $0.25. Construct and interpret a 95% confidence interval for the true mean of the gas price.

Of 94 adults selected randomly from one town, 62 have health insurance. Find a 90% confidence...

Of 94 adults selected randomly from one town, 62 have health insurance. Find a 90% confidence interval for the proportion of all adults in the town who have health insurance.

Question