Mathematics, 20.03.2020 01:35 Yommms

Suppose that 34% of the students at a university favor the semester system, 61% favor the quarter system, and 5% have no preference. Is a random sample of 100 students large enough to provide convincing evidence that the quarter system is favored

Answers: 1

Show answers

Answers

Answer from: sharnisefrazier

$z=\frac{0.61 -0.5}{\sqrt{\frac{0.5(1-0.5)}{100}}}=2.2$

p_v =P(z2.2)=0.014

So the p value obtained was a very low value and using the significance level assumed $\alpha=0.05$ we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of students who favor the quarter system is higher than 0.5

Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

$\hat p=0.61$ estimated proportion of interest

p_o=0.7 is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion for quarter system is higher than 0.5.:

Null hypothesis: $p \leq 0.5$

Alternative hypothesis: p 0.5

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 .

Calculate the statistic

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

$z=\frac{0.61 -0.5}{\sqrt{\frac{0.5(1-0.5)}{100}}}=2.2$

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 significance level assumed is $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a right tailedl test the p value would be:

p_v =P(z2.2)=0.014

Answer from: Quest

You would have 15$ left

Answer from: Quest

6hryt%4578855

Another question on Mathematics

Mathematics, 21.06.2019 17:00

Segment xy is dilated through point m with a scale factor of 2. which segment shows the correct result of the dilation

Answers: 1

Answer

Mathematics, 21.06.2019 18:00

Need on this geometry question. explain how you did it.

Answers: 2

Answer

Mathematics, 21.06.2019 21:20

Find the distance from the theater to the library. leave your answer in simplest radical form if necessary. 12 √12 74 √74

Answers: 2

Answer

Mathematics, 21.06.2019 22:00

Luke started a weight-loss program. the first week, he lost x pounds. the second week, he lost pounds less than times the pounds he lost the first week. the third week, he lost 1 pound more than of the pounds he lost the first week. liam started a weight-loss program when luke did. the first week, he lost 1 pound less than times the pounds luke lost the first week. the second week, he lost 4 pounds less than times the pounds luke lost the first week. the third week, he lost pound more than times the pounds luke lost the first week.

Answers: 2

Answer

You know the right answer?

Suppose that 34% of the students at a university favor the semester system, 61% favor the quarter sy...

Questions