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]
2 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]2 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
I will appreciate a quick answer
Elan Coil [88]

Answer:

∠SRQ = 75º, ∠TQR = 75º, ∠TSR = 105º, ∠STQ = 105º

Step-by-step explanation:

Since the quadrilaterals are similar, their corresponding angles are the same.  

3 0
2 years ago
1) A business man gives N18 000,00 to his three children
pashok25 [27]

Answer: The least share is N450000

Step-by-step explanation:

Given that :

Amount shared = N18 00000

Sharing ratio = 5:4:3

Amount shared by each child :

Total ratio = (5 + 4 + 3 )= 12

First share :

(5 / 12) × 1800000 = 750000

Second share :

(4/12) × 1800000 = 600000

Third share:

(3/12) × 1800000 = 450000

The least amount of the three shares is :

N450000

4 0
3 years ago
What is 7/p=8/9? Solve for p
irina [24]

Answer:

Exact form, p = 63/8

decimal form, p = 7.875

Mixed number form, p = 7 7/8

Step-by-step explanation:

Solve for p by cross multiplying

7 0
2 years ago
Read 2 more answers
17x &gt; −17<br><br> Solve for x<br> Your answer must be simplified<br><br> Need help asap
Fantom [35]

Answer:

x > -1

Step-by-step explanation:

Divide each term by 17 and simplify.

Hope this helps,

Davinia.

7 0
3 years ago
Read 2 more answers
What does the phrase as close as two needles on the same twig
Galina-37 [17]
It means that two people are friends, like two peas in a pod
5 0
3 years ago
Other questions:
  • 7 cu. yd. 9 cu. ft. 134 cu. in. + 1 cu. yd. 12 cu. ft. 200 cu. in.
    7·1 answer
  • In Jana's closet she has 5 pairs of black shoes and 11 pairs of leather shoes. Two of her pairs of shoes are both black and leat
    15·1 answer
  • A total of 486 tickets were sold for the school play. They were either adult tickets or student tickets. There were 64 fewer sru
    13·1 answer
  • What number divide evenly into 125 ?
    15·2 answers
  • What 75% of two hundred
    5·1 answer
  • Solve the equation 5w-5+4w-4
    15·1 answer
  • What is 1 inch to 6 feet
    9·2 answers
  • Need number 1 and 2
    9·1 answer
  • Please help<br><br> See the picture <br><br><br> Line A , B , C OR D ?<br><br> Help
    15·2 answers
  • Helpppppp!!!!!!!!!! Plsss
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!