A study was performed to determine the percentage of people who wear life vests while out on the water. A researcher believed that the percentage was different for those who rode jet skis compared to those who were in boats. Out of 400 randomly selected people who rode a jet ski, 86.5% wore life vests. Out of 250 randomly selected boaters, 92.8% wore life vests. Using a 0.10 level of significance, test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat. Let jet skiers be Population 1 and let boaters be Population 2.
Step 2 of 3:
Step 1 of 3:
State the null and alternative hypotheses for the test. Fill in the blank below.
H0Ha: p1=p2: p1⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯p2H0: p1=p2Ha: p1_p2
Step 3 of 3:
Draw a conclusion and interpret the decision.
Compute the value of the test statistic. Round your answer to two decimal places.

Answers

Answer 1

From the test the person wants, and the sample data, we build the test hypothesis, find the test statistic,  and use this to reach a conclusion.

This is a two-sample test, thus, it is needed to understand the central limit theorem and subtraction of normal variables.

Doing this:

The null hypothesis is [tex]H_0: p_1 - p_2 = 0 \rightarrow p_1 = p_2[/tex]The alternative hypothesis is [tex]H_1: p_1 - p_2 \neq 0 \rightarrow p_1 \neq p_2[/tex]The value of the test statistic is z = -2.67.The p-value of the test is 0.0076 < 0.05(standard significance level), which means that there is enough evidence to conclude that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.

-------------------

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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 [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

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.

-------------------------------------

Proportion 1: Jet-ski users

86.5% out of 400, thus:

[tex]p_1 = 0.865[/tex]

[tex]s_1 = \sqrt{\frac{0.865*0.135}{400}} = 0.0171[/tex]

Proportion 2: boaters

92.8% out of 250, so:

[tex]p_2 = 0.928[/tex]

[tex]s_2 = \sqrt{\frac{0.928*0.072}{250}} = 0.0163[/tex]

------------------------------------------------

Hypothesis:

Test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.

At the null hypothesis, it is tested that the proportions are the same, that is, the subtraction is 0. So

[tex]H_0: p_1 - p_2 = 0 \rightarrow p_1 = p_2[/tex]

At the alternative hypothesis, it is tested that the proportions are different, that is, the subtraction is different of 0. So

[tex]H_1: p_1 - p_2 \neq 0 \rightarrow p_1 \neq p_2[/tex]

------------------------------------------------------

Test statistic:

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis.

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_1 - p_2 = 0.865 - 0.928 = -0.063[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0171^2 + 0.0163^2} = 0.0236[/tex]

The value of the test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-0.063 - 0}{0.0236}[/tex]

[tex]z = -2.67[/tex]

The value of the test statistic is z = -2.67.

---------------------------------------------

p-value of the test and decision:

The p-value of the test is the probability that the proportion differs by at at least 0.063, which is P(|z| > 2.67), given by 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(standard significance level), which means that there is enough evidence to conclude that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.

A similar question is found at https://brainly.com/question/24250158


Related Questions

find the specified lengths and measures. Given: ΔABC≅ΔDEF Find: AB and m∠F

Answers

Answer:

Step-by-step explanation:

solve 3x-4=√(2x^2-2x+2)

Answers

Answer:

Step-by-step explanation:

Begin the solution by squaring both sides of the given equation.  We get:

(3x - 4)^2 = 2x^2 - 2x + 2, or:

9x^2 - 24x + 16 = 2x ^2 - 2x + 2

Combining like terms results in:

7x^2 - 22x + 14 = 0

and the coefficients are a = 7, b = -22, c = 14, so that the discriminant of the quadratic formula, b^2 - 4ac becomes (-22)^2 - 4(7)(14) = 92

According to the quadratic formula, the solutions are

       -b ± √discriminant           -(-22) ± √92             22 ± √92

x = ------------------------------- = ----------------------- = ------------------------

                   2a                                   14                            14

Three ducks and two ducklings weigh 32 kg. Four ducks and three ducklings weigh 44kg. All ducks weigh the same and all ducklings weigh the same. What is the weight of two ducks and one duckling?

Answers

Answer:

20kg

Step-by-step explanation:

Let the weight of one duck be x and the weight of one duckling be y

ATQ, 3x+2y=32 and 4x+3y=44, solving for x and y we get, weight of one duck is 8kg and one duckling is 4kg. The weight of two ducks and one duckling is 20kg

urgent image below for the question

Answers

Answer:

240 ft²

Step-by-step explanation:

Surface area of a rectangular prism is,

2(lw+wh+hl)

= 2(7×6+6×6+6×7)

= 240 ft²

A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 66 types of drinks to choose from, 33 types of sandwiches, and 44 types of chips. How many different value meal packages are possible

Answers

36 different value meal packages are possible

Step-by-step explanation:

To answer this question, multiply all given numbers together.

4*3*3

12*3

36

The area of a square is 64 cm2 then find it's perimeter.​

Answers

Answer:

32cm

Step-by-step explanation:

The area of sqaure is a^2

Side will be

underroot of 64 =8

Premeter of sqaure is 4a = 4×8 = 32cm

first we need to find length.

here.

Area= 64cm^2

or, 64= l^2

using formula area = length × length

therefore solving we get ,

length = 8 cm.

now,

perimeter = 4l

= 4 × 8 cm.

= 32 cm..........

4.Siti and Janice spent 3h 25min altogether in Shopping malls A and B. If they spent 1h 45min in Shopping mall A, how long did they spend in Shopping mall B?

Answers

Answer:

1 hour and 40 minutes

Step-by-step explanation:

→ Convert 3 hr and 25 minutes to minutes

( 3 × 60 ) + 25 = 205 minutes

→ Convert 1 hr and 45 minutes to minutes

( 1 × 60 ) + 45 = 105 minutes

→ Minus the answers from each other

205 - 105 = 100 minutes

→ Convert 100 minutes to hours and minutes

1 hour and 40 minutes

What is 17,210,000,000 written in scientific notation?

Answers

Answer and Step-by-step explanation:

The answer is 1722.1 x [tex]10^8[/tex]

#teamtrees #PAW (Plant And Water)

Answer:

1.72x10^10

Step-by-step explanation:

POSITIVE EXPONENT: means a number is huge

NEGATIVE EXPONENT: indicates a number is teeny-tiny

A(6, -5) and B(-1, 2) in the ratio of 2:5​

Answers

Answer:

p(x,y)= (4,-3)

Step-by-step explanation:

all explainations are in the picture below.

What is the Width of 6.36-9.24

Answers

Answer:

-2.88

Step-by-step explanation:

6.36-9.24= -2.88

which graph represents the absolute value of -3​

Answers

[tex]\sf\huge\underline\color{pink}{༄Answer:}[/tex]

Slope: 0

y - intercept: (0, -3)

Kindly click the attached photo ^^

[tex]\color{pink}{==========================}[/tex]

#CarryOnLearning

[tex]\sf\color{pink}{༄⁂✰Bae \: Yoonah}[/tex]

can yall answer it in the box like the numbers

Answers

Answer:

Hi!

Step-by-step explanation:

1234567890987654211234567890......

Step-by-step explanation:

12345678890098764321

what is symmetrical line​

Answers

Answer:

assuming youre asking for line of symmetry, it's a line that cuts a shape exactly in half.  

for example, a square has 4 lines of symmetry

Please help me with this

Answers

Answer:

6

Step-by-step explanation:

c(2)=(-9/2)*(-4/3)^(2-1)=(-9/2)*(-4/3)=6


The length of a rectangle is 4 units more than its width. The area of the rectangle is 25 more than 4 times the
width. What is the width of the rectangle?
A А 9
B -5
С. 3
D 5
Please select the best answer from the choices provided

Answers

Answer:

D

Step-by-step explanation:

let the width = w

w = w

L = 4 + w

Area = 4*w + 25 = L * w

4w + 25 = L * w                  Substitute for the length

4w + 25 = (w*(w + 4))

4w + 25 = w^2 + 4w          Subtract 4w from each side

w^2 = 25                            Take the square root.

w = +/- 5

- 5 has no meaning.

w = 5

y=4.5x+13.45 y=6x-4.55

Answers

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(

12

,

67.45

)

Equation Form:

x

=

12

,

y

=

67.45

I need to know this answe ASAP

Answers

Answer:

look at the value of f(x) carefully when we put 7 from x the x take 2 value

Step-by-step explanation:

And g(x) function take 4 value. please look at the first option it has extra 2 so 2 plus 2 equal to 4 this means that the answer might be A. But look at D option it multiply by 2 so D option might be correct answer but we need some info and I want to continue. When I put 1 from x f(x)=1 and g(x)= 2 but when we look at the first option it is 1+2 equal to 3 but it must be 2 so the correct answer is not A and the correct answer is D

Simone invests $2,000 in an account that compounds interest quarterly and earns 9%. How many years will it take for his money to double? (Round your answer to one decimal place.)

Answers

no te puedo contestarte yo no hablo inglés

Find the assessed value of a store with a market value of $ 163,000
if the rate for assessed value is 25​% of market value.

Answers

9514 1404 393

Answer:

  $40,750

Step-by-step explanation:

Leaving out the extra words, the question is asking you to find 25% of $163,000.

  0.25 × $163,000 = $40,750

The assessed value is $40,750.

Given that,

→ Rate for assessed value = 25%

→ Market value = $ 163,000

We have to find,

→ 25% of $ 163,000

Then value of 25% is,

→ 25 ÷ 100

→ 0.25

Let's find the assessed value,

→ 25% × $ 163,000

→ 0.25 × 163,000

→ 40750

Thus, $ 40750 is assessed value.

a/(b+ce^x) dx = ? Please solve this

Answers

Answer:

1/ab en (c/be^-x+c)

Step-by-step explanation:

Sure is a harsh question! Here's my Explanation

b+ce^x = t

ce^x an = dt

e^xan = dt/c

an = dt/ce^x = dt/c(t-b/c) = at/(t-b)

en = t-b/c

A/b+ce^x dx = a/t dt/t-b

a ∫1/t (t-b) dt = 1/a∫ (1/(t-b) - 1/t) dt

= 1/ab [∫1/(t-b) dt + ∫-1/t dt]

= 1/ab [en (t-b) - en(t)]

= 1/ab en ((t-b)/t)

t = b + ce^x

= 1/ab en (b+ce^x -b/b+ce^x)

=1/ab en (ce^x/b+ce^x)

= 1/ab en (c/be^-x+c)

F(x) = 3x+5 G(x)= 4x^2-2 H(x) = x^2-3x+1 Find f(x) +g(x) -h(x)

Answers

Answer:

Step-by-step explanation:

f(x) + g(x) = 3x + 5 + 4x^2 - 2

f(x) + g(x) = 4x^2 + 3x + 3

f(x) + g(x) - h(x) = 4x^2 + 3x + 3 - (x^2 - 3x + 1)  Remove the brackets.

f(x) + g(x) - h(x) = 3x^2 +3x + 3 - x^2 + 3x - 1     Collect like terms

f(x)+g(x) - h(x) = 2x^2 + 6x + 2

Answer:

f(x)=3x^2+6x+2

Step-by-step explanation:

What is the image of the point (-7, 4) after a rotation of 180° counterclockwise about the origin?​

Answers

Answer: (7, -4)

Concept:

For each rotation angle, there is a specified rule that could be applied. Please refer to the attachment below for the list of rotation rules.

Solve:

Given point = (-7, 4)

Given rotation rule = (x , y) ⇒ (-x, -y)

(-7, 4) ⇒ (7, -4)

Hope this helps!! :)

Please let me know if you have any questions

5 increased by the product of -3 and a
number x
in algebraic expression

Answers

Answer:

5+(-3x)

Step-by-step explanation:

"5 increased by" means you are going to be adding 5 to something.

"product of -3 and x" means that you multiply -3 by x, creating (-3x)

The given statement "5 increased by the product of -3 and a number x" as an algebraic expression can be written as -3x+5.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given statement "5 increased by the product of -3 and a number x" as an algebraic expression can be written as,

Product of -3 and a number x

⇒ -3 × x = -3x

Product increased by 5,

⇒ -3x + 5

Hence, the given statement "5 increased by the product of -3 and a number x" as an algebraic expression can be written as -3x+5.

Learn more about Expression here:

https://brainly.com/question/13947055

#SPJ2

Expand and simplify the following expressions. a. (2 − 3)( − 6)

Answers

Answer:

your answer should be six I hope this help

Answer:

the should be 6

Step-by-step explanation:

(2-3)(-6)

-12+18

=6

find two number nearest to 8888888 which are exactly divisible by 2915​

Answers

Step-by-step explanation:

Given problem is to find nearest number,

= 8888888/2915

quotient = 3049

remainder= 1053

Now, 2915-1053 = 1862

8888888+1862 = 8890750

8888888-1053 = 8887835

Two numbers nearest to 8888888 which are exactly divisible by 2915 is 8887835 and 8890750

For the z test, the critical region for rejection of H0 _________. Group of answer choices depends on N is determined only by alpha and N allows us to accept the null hypothesis is determined only by alpha

Answers

Answer:

allows us to accept the null hypothesis

Explanation:

The z test(in a normal distribution) score for the critical region determines whether we reject the null hypothesis(H0) or accept the null hypothesis(reject or fail to reject the null hypothesis). If we fail to reject the null hypothesis, then we have accepted the alternative hypothesis (H1). The critical region rejection for z test is calculated using alpha and z score, if z score is greater or less than alpha(positive or negative), we reject the null hypothesis.

Put the following equation of a line into slope-intercept form, simplifying all
fractions.
3x – 9y = -72

Answers

24+-3y is the correct answer

the slope-intercept form of the given equation is y = x/3 + 8.

What is the slope?

The increase divided by the run, or the ratio of the rise to the run is known as the line's slope. The coordinate plane describes the slope of the line.

The slope-intercept form of a line is Y = m*X +C.

Given an equation 3x-9y = -72, which we will try to make in the slope-intercept form by using simplification.

3x-9y = -72

9y = 3x + 72

y = 1/3 * x + 8

Therefore y = x/3 + 8 is the slope-intercept form of the given equation.  where its slope is 1/3.

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ2

5
13


The probabilities that three men win their respective races are 1/3,3/5and 3/4.what is theprobability that
a) all of them win their races)
b) only one of them win his race?

Answers

Answer:

a

Step-by-step explanation:

1/3 x 3/5 x 3/4 =7/12 so therefore that's what the answer isn't

A truck was driven a 140 miles in 3 1/2 hours. If a car is driven the same distance at an average speed of 20 miles an hour faster than the trucks average speed, how long will it take the car.

Answers

Find the speed of the truck:

140 miles / 3.5 hours = 40 miles per hour

The car was 20 miles an hour faster: 40 + 20 = 60 miles per hour.

Divide distance by speed: 140 miles / 60 miles per hour = 2 1/3 hours

Answer: 2 1/3 hours

Answer: 2 2/6 hours

Explanation:

Distance = 140 miles

Time = 3 1/2 hours

= 7/2 hours

Speed = Distance/Time

= 140/(7/2)

= 40 miles

New distance = 140 Miles

New Speed = 60 miles

New Time = 140/60

= 2 2/6 hours

Must click thanks and mark brainliest

Of the respondents, 502 replied that America is doing about the right amount. What is the 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment?

Answers

Answer:

The 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment is (0.461, 0.543), considering [tex]n = 1000[/tex]

Step-by-step explanation:

Incomplete question, so i will suppose this is a sample of 1000.

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Of the n respondents, 502 replied that America is doing about the right amount.

Supposing [tex]n = 1000[/tex], so [tex]\pi = \frac{502}{1000} = 0.502[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.502 - 2.575\sqrt{\frac{0.502*0.498}{1000}} = 0.461[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.502 + 2.575\sqrt{\frac{0.502*0.498}{1000}} = 0.543[/tex]

The 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment is (0.461, 0.543), considering [tex]n = 1000[/tex]

Other Questions
In MNP , point Q is between points M and N, and point R is between points N and P. Point H is the incenter of the triangle, HQMN, and HR NP. QN=36 and HN=39 . What is HR ? Enter your answer in the box. In this fictional map, which elements suggest relative location?Check all that applyA. North and South PigletB West IslandC. Howe StraitD. Whye Strait ASAP please help meeeeeeeee A small object with mass 0.20 kg swings as a pendulum on the end of a long light rope. For small amplitude of swing, the period of the motion is 3.0 s. If the object is replaced by one with mass 0.400 kg, what is the period for small amplitude of swing? (a) 1.5 s (b) 3.05 (c) 6.0 s (d) 12.0 s (e) none of the above answers Since lim n infinity (.............) = ........... Cules son unas razones para visitar a Colombia? (1 point) What was the second capital of the colonies A wire, 20m long, is heated from a temperature of 5C to 55C. If the change in length is 0.020m, calculate the linear expansivity of the wire. How many digits does the flexor digitorum superficialis control? Solve for x. Round to the nearest tenth of a degree, if necessary. Please HELP! Under Section 1557, 2020 Final Rule issued during the Trump Administration sex was initially defined____________ The base and height of a right triangle are 20 inches and 15 inches. Find the length of the hypotenuse. Angels descend from the teaven.(find the antonym of the bold word.) which photo synthetic process can occur at night?A.the reaction at photosystem 1B.the formation of NADHC.the calvin cycle D.the reaction at photosystem 2 When a Select Case statement executes, the value of the test expression is compared with the values that follow each of the _______ keywords. John is a typical student. He usually on the lessons.A.pays attentionB.concentratesC.does D.understands Can someone please help What did Elizabeth Fry do ? 15) Three primary activities of a program are: A) Variables, Operators, and Key Words B) Lines, Statements, and Punctuation C) Input, Processing, and Output D) Integer, Floating-point and Character E) None of the above The Science Club arranged a trip to Smithsonian. Only 2/3 of the members were able to attend, which left one seat empty on the 25-passenger bus. How many members does the Science Club have?