Consider the following data that represents gas mileages per gallon (mpg) of randomly selected cars of a particular brand. 28 32 23 28 24 36 31 34 25 28 29 23 25

A researcher wants to test whether the average gas mileage of this type of car is different from 30 mpg. Compute the p-value.

The p-value is 0.1228.

Step-by-step explanation:

Before testing the hypothesis, we need to find the sample mean and the standard deviation.

Sample of 13:

The sample mean is the sum of all values divided by 13. Using a calculator, it is: X = 28.15.

The sample standard deviation is the square root of the division of the sum of the differences squared between each value and the mean, by the number of values. Using a calculator, we get s = 4.0162.

A researcher wants to test whether the average gas mileage of this type of car is different from 30 mpg.

At the null hypothesis, we test if the average gas mileage is of 30 mpg, that is:

At the alternate hypothesis, we test if the average is different from 30, that is:

The test statistic is:

In which X is the sample mean, is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

30 is tested at the null hypothesis:

This means that

From the sample:

.

Value of the test-statistic:

P-value of the test:

The p-value of the test is the probability that the sample mean differs from 30 by at least |28.15 - 30| = 1.75, which is a two-tailed test with t = -1.66 and 13 - 1 = 12 df.

Using a t-distribution calculator, this p-value is 0.1228.

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source

ok thats very interesting