You are on the market for a new car. You want to check whether there is a significant difference between the fuel economy of mid-size domestic cars and mid-size import cars. You sample 17 domestic car makes and find an average fuel economy of 34.904 MPG with a standard deviation of 4.6729 MPG. For imports, you sample 15 cars and find an average MPG of 28.563 MPG with a standard deviation of 8.4988. Construct a 90% confidence interval for the difference between the true average fuel economies in question. Assume the difference will represent (domestic - import). You can also assume that the standard deviations are statistically the same between the two populations.

Step-by-step explanation:

Hello!

The objective is to test if there is a difference between the fuel economy of mid-size domestic cars and mid-size import cars.

For this there are two samples taken:

X₁: Fuel economy of a domestic car.

Sample 1

n₁= 17 domestic cars

X[bar]₁= 34.904 MPG

S₁= 4.6729 MPG

X₂: Fuel economy of an import car.

Sample 2

n₂= 15 import cars

X[bar]₂= 28.563 MPG

S₂= 8.4988 MPG

To estimate the difference between the average economic fuel of domestic cars and import cars, assuming both variables have a normal distribution and both population variances are unknown but equal, the statistic to use is a t-test for two independent samples with pooled sample variance:

(X[bar]₁-X[bar]₂)±

Sa= 6.73

(34.904-28.563)±

6.341±1.697*2.38

[2.30;10.38]

With a confidence level of 90%, you'd expect that the difference between the average economic fuel of domestic cars and import cars will be contained in the interval [2.30;10.38].

I hope it helps!

Related Questions

the total cost c of buying b cans of beans can be found using the equation c= \$0.79b. What is represented by the dependent variable.

The total cost is represented by the dependent variable.

Step-by-step explanation:

If we have a function:

x is the independent variable and y is the dependent one, since y is a function of x.

In this problem:

So the total cost of buying b cans of beans is 0.79b. That is, the total cost depends of the number of cans of beans bought.

So the total cost is represented by the dependent variable.

Consider the expression 8 – 4 / 2. One student says the answer is 2 and another says it is 6. Which student is correct? Explain what went wrong with the student who made a mistake.

It is 6. The student who got a two did not use order of operations.

Step-by-step explanation:

PEMDAS

You must do division before subtraction. 4/2 = 2.

8 - 2 = 6

Use the complement to find the probability. Enter your answer in simplified fraction form.A spinner has 3 equal sections that are white, green, and blue. What is the probability of not landing on blue?

The probability of not landing on blue is

2/3 or 66.666666...% is the probability of it not landing on blue

Solve for W in the scientific formula c= wtc/1,000

1000/t=w

Step-by-step explanation:

The first thing we need to do is, multiply 1000 to both sides,

c(1000)=wtc

now we need to divide both sides by tc

c(1000))/(tc)=w

The c's on the left side will cancel out

1000/t=w

Step-by-step explanation:

hdhdhdhdhddjdifififiifr

In one full day, a kudzu vine can grow 15 inches in length. How many inches per hour is this?

1.66666666667 inches per hour

0.625

Step-by-step explanation:

15 divided by 24 which equals 0.625

A consumer advocate wants to collect a sample of jelly jars and measure the actual weight of the product in the container. He needs to collect enough data to construct a confidence interval with a margin of error of no more than 3 grams with 95​% confidence. The standard deviation of these jars is usually 3 grams. Estimate the minimum sample size required.

n=3.8416≅4

So Minimum Sample Size is 4

Step-by-step explanation:

In order to find the minimum sample size, the formula we use will be:

Where:

n is sample size

Z is the distribution

S is the standard deviation

E is the  Margin of error

S=3 ,E=3

For Z:

Alpha=1-0.95=0.05

Alpha/2=0.025=2.5%

From Cumulative Standard Distribution Table:

Z at Alpha/2 = 1.960

n=3.8416≅4

So Minimum Sample Size is 4