As part of a study of corporate employees, the director of human resources for pnc inc. wants to compare the distance traveled to work by employees at its office in downtown cincinnati with the distance for those in downtown pittsburgh. a sample of 35 cincinnati employees showed they travel a mean of 370 miles per month. a sample of 40 pittsburgh employees showed they travel a mean of 380 miles per month. the population standard deviations for the cincinnati and pittsburgh employees are 30 and 26 miles, respectively. at the 0.05 significance level, is there a difference in the mean number of miles traveled per month between cincinnati and pittsburgh employees?

Comparing the p value with the significance level we see that so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and a wouldn't be a significant difference in the average of the two groups

Step-by-step explanation:

1) Data given and notation

represent the mean for the sample of Cincinnati

represent the mean for the sample Pittsburgh

represent the population standard deviation for the sample Cincinnati

represent the population standard deviation for the sample Pittsburgh

sample size for the group Cincinnati

sample size for the group Pittsburgh

z would represent the statistic (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:

Null hypothesis:

Alternative hypothesis:

We have the population standard deviation's, so for this case is better apply a z test to compare means, and the statistic is given by:

(1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

3) Calculate the statistic

With the info given we can replace in formula (1) like this:

4) Statistical decision

Since is a bilateral test the p value would be:

Comparing the p value with the significance level we see that so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and a wouldn't be a significant difference in the average of the two groups

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! : )

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