Mathematics, 18.04.2020 02:42, idenneymarie

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 317 people over the age of 55. 70 dream in black and white, and among 296 people under the age of 25. 12 dream in black and white.

Use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under

a. Test the claim using a hypothesis test.

b. Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25. What are the null and alternative hypotheses for the hypothesis test?

Answers: 3

Show answers

Answers

answered: jeffffffff

Step-by-step explanation:

Hello!

The objective is to compare if the proportion of people over 55 years old that dream in black and white is greater than the proportion of those under the age fo 25 that dream in black and white.

To do the comparison two random samples where taken:

Sample 1:

X₁: Number of people over the age of 55 that dream in black and white of a sample of 317.

n₁= 317

x₁= 70

p₁'= x₁/n₁= 70/317= 0.22

Sample 2

X₂: Number of people under the age of 25 that dream in black and white of a sample of 296

n₂= 296

x₂= 12

p₂'= x₂/n₂= 12/296= 0.04

Pooled sample proportion: $p'= \frac{x_1+x_2}{n_1+n_2}= \frac{70+12}{317+296} = 0.13$

The parameters of interest are the population proportions p₁ and p₂, the claim is that the proportion of people over 55 that dream in black and white is greater than than the proportion of people under 25 that dream in black and white, symbolically: p₁ > p₂

H₀: p₁ ≤ p₂

H₁: p₁ > p₂

α: 0.01

The statistic for this test is the approximation of the standard normal distribution:

$Z= \frac{(p'_1-p'_2)-(p_1-p_2)}{\sqrt{p'(1-p')\frac{1}{n_1} +\frac{1}{n_2} } }$ ≈N(0;1)

$Z_{H_0}= \frac{(0.22-0.04)-0}{\sqrt{0.13(1-0.13)*[\frac{1}{317} +\frac{1}{296} ]} } = 6.62$

The p-value of this test is one-tailed to the right, just as it is the test.

p-value < .00001

The decision rule for the p-value approach is:

If the p-value ≤ α, the decision is to reject the null hypothesis.

If the p-value > α, the decision is to not reject the null hypothesis.

In this case, the decision is to reject the null hypothesis.

Using a level of significance of 1%, there is significant evidence to reject the null hypothesis. Then you can conclude that the population proportion of people over the age of 55 that dreams in black and white is greater than the population of people under the age of 25 that dreams in black and white.

I hope this helps!

answered: Guest

if the probability is 1/12, 75 people will receive a $25 gift card

step-by-step explanation:

answered: Guest

$4\left(625^4\right)\left(y^6\right)$

step-by-step explanation:

given expression is $4\sqrt{625^8y^{12}}$ .

now we need to simplify the given expression $\sqrt{20y^8}$ .

we know that square root is equivalent to the power 1/2. so that means we can take half of the exponents to get the square root of given expression.

$4\sqrt{625^8y^{12}}$

$=4\left(625^8y^{12}\right)^{\frac{1}{2}}$

$=4\left(625^8\right)^{\frac{1}{2}}\left(y^{12}\right)^{\frac{1}{2}}$

$=4\left(625^4\right)\left(y^6\right)$

expanding that will give a very very large number so let's keep answer in exponent form.

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:00, cupcake122016

The classrooms are trying to raise $1,200.00 for charity. mrs. leblanc's class has raised 50%. mr. patel's class has raised $235.14 ms. warner's class has raised 1/3 as much as mrs. leblanc's class. how much more money is needed to reach the goal of $1,200.00?

Answers: 1

continue

Mathematics, 21.06.2019 16:30, jaidenlaine9261

Asequence {an} is defined recursively, with a1 = 1, a2 = 2 and, for n > 2, an = an-1 an-2 . find the term a241. a) 0 b) 1 c) 2 d) 1 2

Answers: 1

continue

Mathematics, 21.06.2019 19:30, allicat133

Awater holding tank measures 105 m long, 50 m wide, and 8 m deep. traces of mercury have been found in the tank, with a concen- tration of 60 mg/l. what is the total mass of mercury in the tank? answer in units of kg.

Answers: 1

continue

Mathematics, 21.06.2019 21:40, dededese2403

Astudy was interested in determining if eating milk chocolate lowered someone's cholesterol levels. ten people's cholesterol was measured. then, each of these individuals were told to eat 100g of milk chocolate every day and to eat as they normally did. after two weeks, their cholesterol levels were measured again. is there evidence to support that their cholesterol levels went down? how should we write the alternative hypothesis? (mud = the population mean difference= before - after)a. ha: mud = 0b. ha: mud > 0c. ha: mud < 0d. ha: mud does not equal 0

Answers: 1

continue

Do you know the correct answer?

A study was conducted to determine the proportion of people who dream in black and white instead of...