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1 year ago

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1 answer:

4 0

For the first interval (-1, 2), f(-1) = f(2), which means that the average rate of change on that interval is zero, so the correct option is A.

<h3>Over which interval the rate of change is zero?</h3>

For a function f(x) we define the average rate of change over the interval (a, b) is defined as:

R = (f(b) - f(a))/(b - a)

Here the function is:

f(x) = x^2 - x -1

And the rate of change will be zero on an interval (a, b) if and only if:

f(b) = f(a).

Notice that the first interval is (-1, 2)

f(-1) = (-1)^2 - (-1) - 1 = 1 + 1 - 1 = 1

f(2) = 2^2 - 2 - 1 = 4 - 2 - 1 =1

Then f(-1) = f(2), which means that the average rate of change on that interval is zero, so the correct option is A.

If you want to learn more about average rate of change:

brainly.com/question/23483858

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$z=\frac{0.28 -0.34}{\sqrt{\frac{0.34(1-0.34)}{116}}}=-1.364$

$p_v =2*P(Z$

The p value obtained was a very high value and using the significance level assumed $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIl to reject the null hypothesis, and we can said that at 5% of significance the proportion of graduates from the previous year claim to have encountered unethical business practices in the workplace is not significant different from 0.34.

Step-by-step explanation:

1) Data given and notation

n=116 represent the random sample taken

X represent the number graduates from the previous year claim to have encountered unethical business practices in the workplace

$\hat p=0.28$ estimated proportion of graduates from the previous year claim to have encountered unethical business practices in the workplace

$p_o=0.34$ is the value that we want to test

$\alpha=0.05$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion is 0.34 or no.:

Null hypothesis: $p=0.34$

Alternative hypothesis: $p \neq 0.34$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.28 -0.34}{\sqrt{\frac{0.34(1-0.34)}{116}}}=-1.364$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z$

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