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
IgorC [24]
3 years ago
13

Refer to the following scenario:You want to see if there is a difference between the exercise habits of Science majors and Math

majors. You survey 135 science majors, and find out that 82 of them regularly exercise. You survey 92 math majors, and find out that 41 of them regularly exercise. You test your hypothesis that the proportions are different at the 1% significance level.1. Which of the following is the correct null hypothesis? A. H0 : A = 0 B. H0 : p = 0 C. H0: P1 = P2 D. H0 : H1 = 12 2. Which of the following is the correct alternative hypothesis? A. H0.: P1 + P2 B. H0 : P1 > P2 C. H0 : Pi + P2 D. H0 : M1 is not equal to M2 3. What is the pooled proportion of Science and Math majors that regularly exercise? 4. What is the p-value of your test? 5. State the conclusion of your test in context?6. What is a 99% confidence interval for the difference in the true proportions of Science and Math majors who regularly exercise?
Mathematics
1 answer:
bekas [8.4K]3 years ago
6 0

Answer:

1. H0: P1 = P2

2. Ha: P1 ≠ P2

3. pooled proportion p = 0.542

4. P-value = 0.0171

5. The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

6. The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

Step-by-step explanation:

We should perform a hypothesis test on the difference of proportions.

As we want to test if there is significant difference, the hypothesis are:

Null hypothesis: there is no significant difference between the proportions (p1-p2 = 0).

Alternative hypothesis: there is significant difference between the proportions (p1-p2 ≠ 0).

The sample 1 (science), of size n1=135 has a proportion of p1=0.607.

p_1=X_1/n_1=82/135=0.607

The sample 2 (math), of size n2=92 has a proportion of p2=0.446.

p_2=X_2/n_2=41/92=0.446

The difference between proportions is (p1-p2)=0.162.

p_d=p_1-p_2=0.607-0.446=0.162

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

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{82+41}{135+92}=\dfrac{123}{227}=0.542

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{0.542*0.458}{135}+\dfrac{0.542*0.458}{92}}\\\\\\s_{p1-p2}=\sqrt{0.001839+0.002698}=\sqrt{0.004537}=0.067

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.162-0}{0.067}=\dfrac{0.162}{0.067}=2.4014

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

\text{P-value}=2\cdot P(z>2.4014)=0.0171

As the P-value (0.0171) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

We want to calculate the bounds of a 99% confidence interval of the difference between proportions.

For a 99% CI, the critical value for z is z=2.576.

The margin of error is:

MOE=z \cdot s_{p1-p2}=2.576\cdot 0.067=0.1735

Then, the lower and upper bounds of the confidence interval are:

LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.162-0.1735=-0.012\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.162+0.1735=0.335

The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

You might be interested in
A number w added to 2.3 is more than 18
DanielleElmas [232]
2.3 + w > 18
-2.3 -2.3
w > 15.7
7 0
3 years ago
5th grade math. correct answer will be marked brainliest.
azamat

Answer:

3 1/3 is your answer.

Step-by-step explanation:

Rewriting equation:

4 + 5/6 - 1 - 1/2

4 - 1 = 3

5/6 - 1/2 = ?

Find the LCD of 5/6 and 1/2 and rewrite to solve.

5/6 - 3/6 = 2/6

2/6 = 1/3

3 + 1/3 = 3 1/3

Whole number: 3

numerator: 1

denominator: 3

7 0
3 years ago
Read 2 more answers
Expanding logarithmic Expression In Exercise,Use the properties of logarithms to rewrite the expression as a sum,difference,or m
ch4aika [34]

Answer:

\ln x+\frac{1}{3}\ln (x^2+1)

Step-by-step explanation:

Consider the given expression is

\ln (x\sqrt[3]{x^2+1})

We need to rewrite the expression as a sum,difference,or multiple of logarithms.

\ln (x(x^2+1)^{\frac{1}{3}})        [\because \sqrt[n]{x}=x^{\frac{1}{n}}]

Using the properties of logarithm we get

\ln x+\ln (x^2+1)^{\frac{1}{3}}         [\because \ln (ab)=\ln a+\ln b]

\ln x+\frac{1}{3}\ln (x^2+1)        [\because \ln (a^b)=b\ln a]

Therefore, the simplified form of the given expression is \ln x+\frac{1}{3}\ln (x^2+1).

6 0
3 years ago
What is -3 - -10 + (|-7| - |8|) =
svetlana [45]

Answer:

6

Step-by-step explanation:

5 0
3 years ago
PLZZZZZZZZZZZ HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!!!!
Digiron [165]
The answer is 51 liters.

Since they have a direct relationship, set up a direct proportion.
17/476=x/1428
476x3 is 1428 so
17x3=51
3 0
3 years ago
Other questions:
  • Help on this one as well
    11·1 answer
  • The bases on a baseball diamond are 90 feet apart. how far is it from home plate to second base?
    11·2 answers
  • In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. The spades and the clubs are black and th
    13·2 answers
  • John's monthly salary is 7,000. If John deposits 0.75 of his paycheck into a savings account. How much money does he put in his
    15·1 answer
  • Mercury orbits the Sun in 87 24/25 Earth days. Venus orbits the Sun in 224 7/10Earth days, and Mars
    10·1 answer
  • If a cylinder has a surface area of 59 square inches and its radius
    10·2 answers
  • Which are equivalent ratios to 1:6
    11·1 answer
  • PLZ HELP Which of these values cannot repersent the probability of an event happening?
    9·1 answer
  • Kaitlyn is remodeling her kitchen the table shows the cost of items she wants to buy with her credit card it Kaitlyn has a $2,00
    11·1 answer
  • Lesson 24
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!