Mathematics, 20.12.2019 19:31 layla07

University personnel are concerned about the sleeping habits of students and the negative impact on academic performance. in a random sample of 377 u. s. college students, 209 students reported experiencing excessive daytime sleepiness (eds).
a. is there sufficient evidence to conclude that more than half of u. s. college students experience eds? use a 5% level of significance.
b. what is a 90% confidence interval estimate for the proportion of all of u. s. college students who experience excessive daytime sleepiness?

Answers: 3

Show answers

Answers

Answer from: BreBreDoeCCx

a) $z=\frac{0.554 -0.5}{\sqrt{\frac{0.5(1-0.5)}{377}}}=2.097$

p_v =P(Z2.097)=0.018

If we compare the p value obtained and the significance level given $\alpha=0.05$ 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 reported experiencing excessive daytime sleepiness (EDS) is significantly higher than 0.5 or the half.

b) The 90% confidence interval would be given by (0.512;0.596)

Step-by-step explanation:

Part a

Data given and notation

n=377 represent the random sample taken

X=209 represent the students reported experiencing excessive daytime sleepiness (EDS)

$\hat p=\frac{209}{377}=0.554$ estimated proportion of students reported experiencing excessive daytime sleepiness (EDS)

p_o=0.5 is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

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 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:

$z=\frac{0.554 -0.5}{\sqrt{\frac{0.5(1-0.5)}{377}}}=2.097$

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 provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

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

p_v =P(Z2.097)=0.018

Part b

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$t_{\alpha/2}=-1.64, t_{1-\alpha/2}=1.64$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.554 - 1.64\sqrt{\frac{0.554(1-0.554)}{377}}=0.512$

$0.554 + 1.64\sqrt{\frac{0.554(1-0.554)}{377}}=0.596$

The 90% confidence interval would be given by (0.512;0.596)

Answer from: Quest

.25

step-by-step explanation:

Answer from: Quest

Ithink it’s b because it say 3 plastic rings and all the balls

Another question on Mathematics

Mathematics, 20.06.2019 18:04

Me find the missing dimension of a triangle height: 7 in., area: 21^2

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

What is the slope of the line shown below?

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

Sara has 2 2/3 cup taco meat. she needs 1/6 cup to make one taco. how many tacos can sara make with the taco meat she has?

Answers: 1

Answer

Mathematics, 22.06.2019 01:00

Pleasse me i need an answer. give me the correct answer. answer if you know it ! the club will base its decision about whether to increase the budget for the indoor rock climbing facility on the analysis of its usage. the decision to increase the budget will depend on whether members are using the indoor facility at least two times a week. use the best measure of center for both data sets to determine whether the club should increase the budget. assume there are four weeks in a month. if you think the data is inconclusive, explain why.

Answers: 3

Answer

You know the right answer?

University personnel are concerned about the sleeping habits of students and the negative impact on...

Questions