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
Harman [31]
3 years ago
6

AT&T would like to test the hypothesis that the proportion of 18- to 34-year-old Americans that own a cell phone is less tha

n the proportion of 35- to 49-year-old Americans. A random sample of 200 18- to 34-year-old Americans found that 126 owned a smartphone. A random sample of 175 35- to 49-year-old Americans found that 119 owned a smartphone. If Population 1 is defined as 18- to 34-year-old Americans and Population 2 is defined as 35- to 49-year-old Americans, the correct hypothesis statement for this hypothesis test would be
Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
5 0

Answer:

The null and alternative hypothesis can be written as:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans.

This claim will be reflected in the alternnative hypothesis, that will state that the population proportion 1 (18 to 34) is significantly smaller than the population proportion 2 (35 to 49).

On the contrary, the null hypothesis will state that the population proportion 1 is ot significantly smaller than the population proportion 2.

Then, the null and alternative hypothesis can be written as:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0

The significance level is assumed to be 0.05.

The sample 1, of size n1=200 has a proportion of p1=0.63.

p_1=X_1/n_1=126/200=0.63

The sample 2, of size n2=175 has a proportion of p2=0.68.

p_2=X_2/n_2=119/175=0.68

The difference between proportions is (p1-p2)=-0.05.

p_d=p_1-p_2=0.63-0.68=-0.05

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{126+119}{200+175}=\dfrac{245}{375}=0.653

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.653*0.347}{200}+\dfrac{0.653*0.347}{175}}\\\\\\s_{p1-p2}=\sqrt{0.001132+0.001294}=\sqrt{0.002427}=0.049

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.05-0}{0.049}=\dfrac{-0.05}{0.049}=-1.01

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

\text{P-value}=P(z

As the P-value (0.1554) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans.

You might be interested in
An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corne
lawyer [7]

Answer:

The dimensions of the resulting box that has the largest volume is 1.3 inches x 1.3 inches

Step-by-step explanation:

Card board size is L= 14 inches and

W = 6 inches

Let x be the size of equal squares cut from 4 corners and bent into a box whose size is now;

L = 14 − 2x , W = 6 −2x and h = x inches.

Volume of the box is given as;

V = (14 −2x)(6−2x)x

V =(4x² − 40x + 84)x

= 4x³ − 40x² + 84x.

Now, for the maximum value,

dV/dx =0

Thus,

dv/dx = 12x² - 80x + 84 = 0

Using quadratic formula

x = [-(-80) ± √(-80²) - 4(12 x 84)]/(2 x 12)

x = [80 ± √(6400 - 4032)]/24

x = (80 + 48.66)/24 or (80-48.66)/24

x = 5.36 or 1.31

Looking at the two values, 1.31 would be more appropriate because if we use 5.36,we will get a negative value of the width (W).

Thus, x = 1.31 inches

Let us use the Second Derivative Test to verify that V has a local maximum at x = 1.31.

Thus;

d²v/dx² = 24x - 80 = 24(1.31) - 80 = -48.56

This is less than 0 and therefore, the volume of the box is maximized when a 1.31 inch by 1.3 inch square is cut from the corners of the cardboard sheet.

3 0
3 years ago
Hurry please<br> I need the answer to this one in 2 minutes
adoni [48]

Answer:

125

Step-by-step explanation:

45 ÷9=5

5² or 5×5=25

25×5=125

Hope this helps!

7 0
2 years ago
Read 2 more answers
Anna bowled 5 games today. All of her scores were within 15 pins of her average score of 222. The absolute value equation that c
KiRa [710]

Answer:

237

Step-by-step explanation:

7 0
3 years ago
For the right triangle shown, the lengths of two sides are given. find the third side. leave your answer in simplified, radical
lisov135 [29]
If c is the hypotenuse and b is the leg, then the third side (a):
a= \sqrt{c^2-b^2}= \sqrt{16^2-9^2}= \sqrt{256-81}= \sqrt{175}=5 \sqrt{7}

If b and с are legs, then hypotenuse (a):
a= \sqrt{b^2+c^2}= \sqrt{9^2+16^2}= \sqrt{81+256}= \sqrt{337}
3 0
2 years ago
Read 2 more answers
What is 3x7/10 I need help as soon a possible homework is due tomorrow
Strike441 [17]

Answer:

\frac{3 \times 7}{10}  =  \frac{21}{10}

6 0
2 years ago
Other questions:
  • 20 POINTS<br> Please answer the question in the photo
    14·1 answer
  • A rocket is launched into the air. The projectile motion of the rocket can be modeled using h(t) = 112t –16t2, where t is the ti
    8·2 answers
  • Write a verbal expression for 73
    11·2 answers
  • Can u guys help me pls
    13·1 answer
  • A stock valued at $100 decreases in value by 9.5% each year? What is the function?
    12·1 answer
  • Maya has already run 1 mile on her own, and she expects to run 1 mile during each track practice. How many miles would Maya have
    14·1 answer
  • An aquarium tank in the shape of a rectangular prism is 56 cm long, 29 cm wide, and 24 cm high. The top of the tank is open, and
    13·1 answer
  • Suppose you put two white socks and one brown sock in a bag and you
    5·1 answer
  • Solve the system using elimination. Show your work! (6 pts)<br> (7x + 10y = 11<br> (4x + 3y = -10
    8·1 answer
  • Find the area of the figure. Round to the nearest hundredth where necessary.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!