Mathematics, 14.02.2020 04:45 gunnatvinson

A study was recently conducted at a major university to estimate the difference in the proportion of business school graduates who go on to graduate school within five years after graduation and the proportion of non-business school graduates who attend graduate school. A random sample of 400 business school graduates showed that 75 had gone to graduate school while in a random sample of 500 non-business graduates, 137 had gone on to graduate school. Based on a 95 percent confidence level, what is the upper limit of the confidence interval estimate? Round to three decimal places.

Answers: 2

Show answers

Answers

Answer from: madi1820

$(0.274-0.1875) - 1.96 \sqrt{\frac{0.274(1-0.274)}{500} +\frac{0.1875(1-0.1875)}{400}}=0.0318$

$(0.274-0.1875) + 1.96 \sqrt{\frac{0.274(1-0.274)}{500} +\frac{0.1875(1-0.1875)}{400}}=0.141$

And the 95% confidence interval would be given (0.032;0.141).

We are confident at 95% that the difference between the two proportions is between $0.032 \leq p_A -p_B \leq 0.141$

The upper bound would be 0.141.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

p_B represent the real population proportion of business school graduates who go on to graduate school within five years after graduation

$\hat p_B =\frac{75}{400}=0.1875$ represent the estimated proportion of business school graduates who go on to graduate school within five years after graduation

n_B=400 is the sample size

p_A represent the real population proportion of non-business school graduates who attend graduate school

$\hat p_A =\frac{137}{500}=0.274$ represent the estimated proportion of non-business school graduates who attend graduate school

n_A=500 is the sample size required for Brand B

represent the critical value for the margin of error

The population proportion have the following distribution

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

Solution to the problem

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$(0.274-0.1875) - 1.96 \sqrt{\frac{0.274(1-0.274)}{500} +\frac{0.1875(1-0.1875)}{400}}=0.0318$

$(0.274-0.1875) + 1.96 \sqrt{\frac{0.274(1-0.274)}{500} +\frac{0.1875(1-0.1875)}{400}}=0.141$

And the 95% confidence interval would be given (0.032;0.141).

We are confident at 95% that the difference between the two proportions is between $0.032 \leq p_A -p_B \leq 0.141$

The upper bound would be 0.141.

Answer from: Quest

the bottom of the spinner is not flat.

step-by-step explanation:

Answer from: Quest

You shouldn’t be using this website cheater

Another question on Mathematics

Mathematics, 20.06.2019 18:04

Write each expression in exponential form and find its value. 2 x 2 x 2 x 2

Answers: 2

Answer

Mathematics, 22.06.2019 01:30

5cakes cost 3.50 how much do 7 cakes cost

Answers: 2

Answer

Mathematics, 22.06.2019 03:30

Aking and his army will attempt to capture a fortress. the left and right flanks break off from the main group to attack the west and east guard towers. suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another. if both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. if, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. if both flanks fail, then the king's chance of capturing the fort drops to 20%. it turns out the king captures the fort. what is the probability that one, and only one, flank was successful (either the left, or the right, but not both)? (round your answer to 3 decimal places)

Answers: 2

Answer

Mathematics, 22.06.2019 04:10

Which expression is equivalent to the square root of 2 multipllied by 5 divided by 18

Answers: 2

Answer

You know the right answer?

A study was recently conducted at a major university to estimate the difference in the proportion of...

Questions

Mathematics, 22.04.2020 15:48

Un padre tiene 37 años y Las edades de sus tres hijos suman 25 años dentro de Cuántos años a las edades de los hijos sumarán como la edad del padre...

Mathematics, 22.04.2020 15:48