The average stopping distances for a population of school buses traveling 50 miles per hour, measured...

The average stopping distances for a population of school buses traveling 50 miles per hour, measured in feet, are normally distributed, with a standard deviation of 6 feet. Using a random sample of 23 buses having a sample mean of 262 feet, construct a 95% confidence interval for the mean stopping distance of the population.

Solutions

Expert Solution

Solution :

Given that,

= 50

s =6

n = Degrees of freedom = df = n - 1 = 23 - 1 = 22

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2= 0.05 / 2 = 0.025

t /2,df = t0.025,22 = 2.074 ( using student t table)

Margin of error = E = t/2,df * (s / $\sqrt$ n)

= 2.074 * ( 6/ $\sqrt$ 23)

= 2.59

The 95% confidence interval mean is,

- E < < + E

50 - 2.59 < < 50+ 2.59

47.41 < < 52.59

(47.41 , 52.59)

orchestra answered 2 years ago

Next > < Previous

Related Solutions

5.1 A car is traveling along a highway at 65 miles per hour. The road is...

5.1 A car is traveling along a highway at 65 miles per hour. The road is horizontal (0% slope). If the wind resistance and rolling resistance at the wheels creates a combined resistive force of 950 N, what is the power (kW) developed at the rear wheels? 5.2 How much power (kW) must the car engine in problem 5.1 develop if the overall mechanical efficiency of the transmission and drive train is 94%? 5.3 Assume the car engine in problem...

When traveling 40 mph (miles per hour), the distance that it takes Fred’s car to stop...

When traveling 40 mph (miles per hour), the distance that it takes Fred’s car to stop varies evenly between 120 and 155 feet. (This includes the reaction distance and the braking distance.) All of the questions are related to the stopping distance when Fred is traveling 40 mph. a) Let S be the distance it takes for Fred’s car to stop at when traveling 40 mph. Find the distribution, parameter(s), and support of S. b) What is the probability that...

Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a...

Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. Use the two-sample t test at significance level 0.01 to test H0: μ1 − μ2 = −10 versus Ha: μ1 − μ2 < −10 for the following data: m = 6, x = 114.8, s1 = 5.05, n = 6, y = 129.4, and s2 = 5.33. Calculate the test statistic and determine the...

Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a...

Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. Use the two-sample t test at significance level 0.01 to test H0: μ1 − μ2 = −10 versus Ha: μ1 − μ2 < −10 for the following data: m = 7, x = 114.5, s1 = 5.06, n = 7, y = 129.9, and s2 = 5.38. Calculate the test statistic and determine the...

Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a...

Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: m = 10, x = 116.8, s1 = 5.28, n = 7, y = 129.6, and s2 = 5.47. Calculate a 99% CI for the difference between true average stopping distances for cars equipped with system 1 and cars equipped with system 2. (Give answers accurate to 2 decimal places.) Lower...

Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a...

Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: m = 8,x = 115.8, s1 = 5.06, n = 8, y = 129.5, and s2 = 5.35. Calculate a 95% CI for the difference between true average stopping distances for cars equipped with system 1 and cars equipped with system 2. (Round your answers to two decimal places.)

A researcher claims that the average wind speed in his city is 10 miles per hour....

A researcher claims that the average wind speed in his city is 10 miles per hour. In a random sample of 36 days, you found the average speed of wind is 10.2 with a standard deviation of 0.8 miles per hour. At α=0.05 is there enough evidence to say that the average is greater than the researcher’s claim. Show your work by using hypothesis testing.

The average annual wind speed in Rochester, Minnesota is 13.1 miles per hour. A sample of...

The average annual wind speed in Rochester, Minnesota is 13.1 miles per hour. A sample of 100 days is used to determine the average wind speed. Find the 98% confidence interval of the mean. Assume the standard deviation was 2.8 miles per hour.

Would a person traveling at a constant 500 miles an hour feel a greater amount of...

Would a person traveling at a constant 500 miles an hour feel a greater amount of force than a person traveling at a constant 50 miles an hour? Why or why not?

You collect the following data on the average speed (in miles per hour) of a student driver on the highway:

You collect the following data on the average speed (in miles per hour) of a student driver on the highway:Speed68666982838275798679807977597372715173100738080677270676875666387726269587478736773798475656568786460857782867487100777175727276587663767266737983848678787764657868819286568483a.If you want to construct a 95% confidence interval, what would use for the t-critical value?b. what would be the lower boundof your 95% confidence interval?c. what would be the upper bound of your 95% confidence interval?

Subjects