1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
gulaghasi [49]
3 years ago
5

In a large midwestern university (the class of entering freshmen is 6000 or more students), an SRS of 100 entering freshmen in 1

999 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 2000. In 2001, an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. Let p1 and p2 be the proportion of all entering freshmen in 1999 and 2001, respectively, who graduated in the bottom third of their high school class.
Required:
Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared with the proportion in 1999
Mathematics
1 answer:
Serga [27]3 years ago
5 0

Answer:

The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

1999:

20 out of 100 in the bottom third, so:

p_1 = \frac{20}{100} = 0.2

s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04

2001:

10 out of 100 in the bottom third, so:

p_2 = \frac{10}{100} = 0.1

s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03

Test if proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

At the null hypothesis, we test if the proportion is still the same, that is, the subtraction of the proportions in 1999 and 2001 is 0, so:

H_0: p_1 - p_2 = 0

At the alternative hypothesis, we test if the proportion has been reduced, that is, the subtraction of the proportion in 1999 by the proportion in 2001 is positive. So:

H_1: p_1 - p_2 > 0

The test statistic is:

z = \frac{X - \mu}{s}

In which X is the sample mean, \mu is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that \mu = 0

From the two samples:

X = p_1 - p_2 = 0.2 - 0.1 = 0.1

s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05

Value of the test statistic:

z = \frac{X - \mu}{s}

z = \frac{0.1 - 0}{0.05}

z = 2

P-value of the test and decision:

The p-value of the test is the probability of finding a difference of at least 0.1, which is the p-value of z = 2.

Looking at the z-table, the p-value of z = 2 is 0.9772.

1 - 0.9772 = 0.0228.

The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

You might be interested in
Whats equivalent to 1/5
Juli2301 [7.4K]
To find equivalent numbers you multiply the top and bottom by the same number. Examples are: 2/10 (by 2), 3/15 (by 3), 4/20 (by 4), etc.

1 * 9 = 9
------------
5 * 9 = 45

So another is 9/45

hope it helps!
5 0
3 years ago
Solve for x: 2 logz 2x = 6
Nikolay [14]

Answer:

x=3

Step-by-step explanation:

if the equation is 2x=6 then you'd do 6/2 and 2x/2 to cancel out the 2 and get x=3

5 0
3 years ago
Least to greatest 0.4, 5/8, 74%, 3/5
SashulF [63]

Answer:

0.4,3/5,5/8,74%

Step-by-step explanation:

Change them all into decimals.

Get 0.4,0.625,0.74,0.6

Then reorder and see what their original values were

5 0
3 years ago
The delivery ramp at the corner cafe id a right triangle. The hypotenuse is 4 meters long. One leg is 3 meters long. What is the
disa [49]

Answer:

f. sqrt 7 meters

Step-by-step explanation:

we use Pythagoras' theorem here,

let the unknown side be x,

therefore,

=> 3² + x² = 4²

=> x² = 16 - 9

=> x = √7 m

7 0
3 years ago
Read 2 more answers
URGENT!!!! WILL GIVE BRANLIEST PLS HELP OR AT LEAST TAKE A LOOK!! I HAVE LESS THEN 10 MINUTES LEFT PLS!!!! IM LOOSING HOPE! SHAR
Sindrei [870]

Answer:

Ok

Step-by-step explanation:

:DDD

4 0
3 years ago
Other questions:
  • What are both of the zeros of x^2=10x-24
    8·1 answer
  • A deposit of $20,000 is placed in a scholarship fund that earns an annual interest rate of 2.25% compounded daily. Find the valu
    7·1 answer
  • Change the following equation to slope, intercept form 3x-y=5. show your work​
    7·2 answers
  • Adjacent angles of intersecting lines are complementary angles. true false
    5·2 answers
  • The profit that the vendor makes per day by selling x pretzels is given by the function P(x) = -0.004 x^2 + 2.8x - 350. Find the
    7·1 answer
  • If you averaged 400 miles a day how many miles would it take to go 1990 miles?
    5·2 answers
  • Which of the following represents the graph of the equation y = -2x + 1?
    15·2 answers
  • The vertices of rectangle ‘ABCD’ are A(3, 1), B(-5, 1),
    15·2 answers
  • Help me :p . :] And ty if you do.​
    6·2 answers
  • Maxine types 294 words in 7 minutes. How many words does Maxine type in 11 minutes?<br> 352 words
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!