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
ladessa [460]
3 years ago
8

A survey of 1100 adults from a certain region​ asked, "If purchasing a used car made certain upgrades or features more​ affordab

le, what would be your preferred luxury​ upgrade?" The results indicated that 49​% of the females and 41​% of the males answered window tinting. The sample sizes of males and females were not provided. Suppose that of 600 ​females, 294 reported window tinting as their preferred luxury upgrade of​choice, while of 500 ​males, 205 reported window tinting as their preferred luxury upgrade of choice. Complete parts​ (a) through​ (d) below.
a. Is there evidence of a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade at the 0.05
level of​ significance?
b. State the null and alternative​hypotheses, where π1 is the population proportion of females who said they prefer window tinting as a luxury upgrade and π2 is the population proportion of males who said they prefer window tinting as a luxury upgrade.
Mathematics
1 answer:
Sergio039 [100]3 years ago
6 0

Answer:

a) The p-value of the test is 0.0076 < 0.05, which means that there is evidence of a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade at the 0.05.

b) The null hypothesis is H_0: \pi_1 - \pi_2 = 0 and the alternate hypothesis is H_1: \pi_1 - \pi_2 \neq 0.

Step-by-step explanation:

Before testing the hypothesis, 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.

Females:

49% from a sample of 600. So

\pi_1 = 0.49, s_{\pi_1} = \sqrt{\frac{0.49*0.51}{600}} = 0.0204

Males:

41% from a sample of 500. So

\pi_2 = 0.41, s_{\pi_2} = \sqrt{\frac{0.41*0.59}{500}} = 0.022

Test if there is a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade.

From here, question b can already be answered.

At the null hypothesis we test if there is no difference, that is, the subtraction of the proportions is 0. So

H_0: \pi_1 - \pi_2 = 0

At the alternate hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0. So

H_1: \pi_1 - \pi_2 \neq 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 = \pi_1 - \pi_2 = 0.49 - 0.41 = 0.08

s = \sqrt{s_{\pi_1}^2 + s_{\pi_2}^2} = \sqrt{0.0204^2 + 0.022^2} = 0.03

Value of the test statistic:

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

z = \frac{0.08 - 0}{0.03}

z = 2.67

Question a:

P-value of the test and decision:

The p-value of the test is the probability that the sample proportion differs from 0 by at least 0.08, which is P(|Z| > 2.670, which is 2 multiplied by the p-value of Z = -2.67.

Looking at the z-table, Z = -2.67 has a p-value of 0.0038.

2*0.0038 = 0.0076

The p-value of the test is 0.0076 < 0.05, which means that there is evidence of a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade at the 0.05.

You might be interested in
What is the LCM for 9 and 12
Serhud [2]
36! goodluck hope it good
8 0
2 years ago
Jake was taking a tip from to san Antonio. the total distance of the trip is 274 miles. after driving 107 miles he stopped for l
Korvikt [17]
He has 167miles left
7 0
3 years ago
Read 2 more answers
Problem 4:
Kipish [7]

Answer:

12cm and 16cm

Step-by-step explanation:

The hypotenuse of the right angle triangle  = 20cm

 let the other two sides be x and y;

 The difference;

                x  = y - 4

Problem:

Find x and y;

Solution:

According to the pythagoras theorem;

    x² + y² = 20²  ------ i

       x² + y² = 400 ----- i

and  x - y = 4 ---- ii

So;   x = 4 + y

Now input the value into equation (i);

  (y + 4)² + y² = 400

   (y+4)(y+4) + y² = 400

    y² + y² + 4y + 4y + 16 = 400

    2y² + 8y + 16 = 400

    2y² + 8y + 16 -400 = 0

   2y² + 8y - 384 = 0;

      y² + 4y - 192 = 0

Factorize the equation;

  y² + 16y - 12y - 192 = 0

  y(y + 16) - 12(y + 16) = 0

  (y-12)(y + 16) = 0

     y -12 = 0 or y+ 16 = 0

     y = 12 or -16

It is not realistic for the length of a body to be a negative value, so y= 12;

   since;

    x - y = 4,

    x = 4 + 12

    x = 16

5 0
3 years ago
A parabola opening up or down has vertex (0,0) and passes through (12, -18). Write its
denis-greek [22]
The equation is y= -1/8x^2
4 0
3 years ago
Complete the statement.<br> L=234 mL
Andru [333]

Answer:

0.234

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • What's (8,-2) (r,-6), m =-4
    10·1 answer
  • Rename the number <br> 25,600=_______?
    10·1 answer
  • A bicycle tire is 28 inches in diameter. Approximately how far does the bicycle move forward each time the wheel goes around? (u
    8·1 answer
  • (6k^4-k^3-8k)-(5k^4+6k-8k^3)​
    12·2 answers
  • 401(&lt;) the contributions are tax deductible, and income generated by the account is
    9·1 answer
  • Find the volume of a right circular cone that has a height of 19.5 m and a base with a
    11·2 answers
  • (need help ASAP!!! PLS) Are these answers correct?
    10·2 answers
  • Two consecutive integers have a sum of 53. Find the integers.
    13·1 answer
  • The vertex is (-8,- 4) and the parabola opens up.<br> The domain of f is?
    10·1 answer
  • Given g(x)=-x+4g(x)=−x+4, find g(5)g(5) whats the answer?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!