Mathematics, 25.03.2020 06:24 maxi12312345

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

Answers: 2

Show answers

Answers

Answer from: Neko1kat

$(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412$

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

And the upper limit would be -0.0318

Step-by-step explanation:

Assuming this complete question :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?

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".

p_A represent the real population proportion for graduate school

$\hat p_A =\frac{75}{400}=0.1875$ represent the estimated proportion for graduate school

n_A=400 is the sample size required for graduate school

p_B represent the real population proportion for non graduate school

$\hat p_B =\frac{137}{500}=0.274$ represent the estimated proportion for non graduate school

n_B=500 is the sample size required for non graduate school

represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution

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

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:

$(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412$

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

And the upper limit would be -0.0318

Answer from: Quest

109 trust me

step-by-step explanation:

Answer from: Quest

hi there!

the answer to this question is d: 35

step-by-step explanation:

5 to the power of 2 is 25

2 multiplied by 5 is 10

then you add the 2 numbers and you get 35

Another question on Mathematics

Mathematics, 21.06.2019 17:00

Amanager recorded the number of bicycles sold by his company each quarter. his projected sales after t years is given by the expression below. which of the following statements best describes the expression? a. the initial sales of 575 bicycles increases at the rate of 4% over 4 quarters. b. the initial sales of 575 bicycles increases at the rate of 18% over 4 years. c. the initial sales of 575 bicycles increases at the rate of 4% over t quarters. d. the initial sales of 575 bicycles increases at the rate of 18% over t years.

Answers: 1

Answer

Mathematics, 22.06.2019 00:30

Two corresponding sides of two similar triangles are 3cm and 5cm. the area of the first triangle is 12cm2. what is the area of the second triangle?

Answers: 2

Answer

Mathematics, 22.06.2019 03:00

Find the slope of the line that passes through the points (0, 0) and (-2, -3). 2/3 3/2 -3/2

Answers: 2

Answer

Mathematics, 22.06.2019 03:30

The mountain springs water company has two departments, purifying and bottling. the bottling department received 67,000 liters from the purifying department. during the period, the bottling department completed 65,000 liters, including 3,000 liters of work in process at the beginning of the period. the ending work in process was 5,000 liters. how many liters were started and completed during the period?

Answers: 3

Answer

You know the right answer?

Business school graduates showed that 75 had gone to graduate school while in a random sample of 500...

Questions

Mathematics, 06.12.2019 16:31

Find the perimeter of the polygon defined by the coordinates (5, 8), (12, 0), (-5, 0), and (-1, 8). (round to nearest tenth) a) 42.5 units

Mathematics, 06.12.2019 16:31

What if scott bought 3 more stamps and now has 21 stamps? some album pages have 1 stamp and some pages have 2 stamps. show how many different ways he...