The mean income per person in the United States is $41,500, and the distribution of incomes follows a normal distribution. A random sample of 10 residents of Wilmington, Delaware, had a mean of $47,500 with a standard deviation of $10,600. At the .01 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average? (a) State the null hypothesis and the alternate hypothesis.
H0: ? ?
H1: ? >
(b) State the decision rule for .01 significance level. (Round your answer to 3 decimal places.)
Reject H0 if t >
(c) Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic
(d) Is there enough evidence to substantiate that residents of Wilmington, Delaware have more income than the national average at the .01 significance level?

Answers

Answer 1

Answer:

A) Null Hypothesis; H0: μ = $41,500

Alternative hypothesis; H1: μ > $41,500

B) Reject H0 is t > 2.821433

C) t = 1.79

D) there is no sufficient evidence to support the claim that residents of Wilmington, Delaware have more income than the national average

Step-by-step explanation:

A) The hypotheses is given as;

Null Hypothesis; H0: μ = $41,500

Alternative hypothesis; H1: μ > $41,500

B) From online t-score calculator attached using significance level of 0.01 and DF = n - 1 = 10 - 1 = 9, we have;

t = 2.821433

Normally, when the absolute value of the t-value is greater than the critical value, we reject the null hypothesis. However, when the absolute value of the t-value is less than the critical value, we fail to reject the null hypothesis.

Thus, if t > 2.821433, we will reject the null hypothesis H0.

C) Formula for the test statistic is;

t = (x' - μ)/(s/√n)

We have, μ = 41500, x' = 47500, s = 10600, n = 10

t = (47500 - 41500)/(10600/√10)

t = 1.79

D) So, 1.79 is less than the t-critical value of 2.821433. Thus, we will fail to reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that residents of Wilmington, Delaware have more income than the national average

Pre-Solving

We are given that a line has a slope (m) of -2 and passes through (5, -6).

We want to write the equation of the line.

There are three ways to write the equation of the line:

Slope-intercept form, which is y=mx+b, where m is the slope and b the value of y at the y-intercept.
Standard form, which is ax+by=c, where a, b, and c are free integer coefficients.
Point-slope form, which is $y-y_1=m(x-x_1)$ , where m is the slope and $(x_1,y_1)$ is a point.

Any of these forms will work, however let's put it into slope-intercept form as that is the most common way.

Solving

As we are already given the slope, we can immediately plug that into the equation.

Substitute m with -2.

y = -2x + b

Now, we need to solve for b.

As the equation passes through (5, -6), we can use its values to help solve for b.

Substitute 5 as x and -6 as y.

-6 = -2(5) + b

Multiply.

-6 = -10 + b

Add 10 to both sides.

4 = b

Substitute 4 as b.

y = -2x + 4

A report describes the results of a large survey involving approximately 3500 people that was conducted for the Center for Disease Control. The sample was selected in a way that the Center for Disease Control believed would result in a sample that was representative of adult Americans. One question on the survey asked respondents if they had learned something new about a health issue or disease from a TV show in the previous 6 months. Data from the survey was used to estimate the following probabilities, where L-event that a randomly selected adult American reports learning somethlng new about a health Issue or disease from a TV show in the previous 6 months and F-event that a randomly selected adult American is female Assume that P(F) 0.5. Are the events L and F independent events? Use probabilities to justify your answer. Land Flare notindependent events, because P(L) P(F)- 0.3 , which is not equal to P(L n F)

Answers

0.3 - 60 is your right answer!

What is the value of x? *
4x + 32
172°
Your answer

Answers

Answer:

x=35

Step-by-step explanation:

Because the 2 lines are parallel u kno 172=4x+32

from there: 172-32=4x or 140=4x, and then 140/4=x

Final answer:

To solve for 'x' in the equation 4x + 32 = 172, we isolate 'x' by first subtracting 32 from both sides of the equation. This gives us 4x = 140. Then, solving for 'x', we divide both sides by 4, resulting in 'x' equal to 35.

Explanation:

To find the value of x, we need to use the process of algebraic simplification. In the equation provided, isolate x by subtracting 32 from both sides of the equation:

4x + 32 = 172

4x = 172 - 32

4x = 140

Next, solve for x by dividing both sides of the equation by 4:

x = 140 / 4

x = 35

Therefore, the value of x in the equation is 35.

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How do I write 4,332 in scientific notation??

Answers

Answer:

4.332 times 10^3

Step-by-step explanation:

ion kno if thats right but i tried.

Answer:

4.332 x 10 to the 3 power I do believe

Step-by-step explanation:

Find each percent increase. Round to the nearest percent

Answers

Answer:

1. 15 to 21 = 21 - 15 / 15 = 0.4*100% = 40%

2. 12 teachers to 48 teachers = 48 - 12/48 = 0.75 * 100% = 75%

3. 80 pencil to 120 pencil = 120 - 80 / 80 = 0.5*100% = 50%

4. 40 cans to 70 cans = 70 - 40 / 70 = 0.43 * 100% = 43%

Find the parametric and symmetric equations for the line passing through the points P1=(2,2,3) and P2=(1,3,−1) . NOTE: this problem does not have a unique answer unless we specify how to choose the direction vector v (see pages 610 and 611). In order to obtain the required solution for this problem use the vector v=P1−P2 (see page 585). Further, you need to use the given point P1 in the formula. PARAMETRIC: x(t)= y(t)= z(t)= SYMMETRIC: (quotient involving x ) = (quotient involving y) = (quotient involving z ) =

Answers

Answer:

parametric equation: q = (2-t)x + (2+t)y + (3-4t)z

symm equation: $(x-2)/(-1) = (y-2)/(1) = (z-3)/(-4)$

Step-by-step explanation:

Parametric equation is just like the point slope equation:

y= b + mx

but in this case we have multiple variable so it'll be

q= p₀ + dt

p₀ will be any of your point. d will be the vector containing points shared by both your vector. It can be found by subtracting your two points together.

t is just an arbitrary variable.

Solve for d=p₂ - p₁ , you can also do d=p₁ - p₂

Now plug it into your q= p₀ + dt equation.

You can plug p₂ or p₁ in for p₀. I used p₁.

The result should give you the parametric equation.

Now solve for all of them in term of t. This step is just basic algebra.

since they're all t=..., then you can set them all equal to each other to get the symmetric equation.

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The table shows the number, expressed in millions, of citizens who moved in 2004, categorized by where they moved and whether they were an owner or a renter. find the probability, expressed as a decimal rounded to the nearest number of people in a certain country who moved in 2004, in millions moved to same region moved to different region moved to different country owner 11.6 11.6 2.7 2.7 0.4 0.4 renter 18.7 18.7 4.5 4.5 1.0 1.0 hundredth, that a randomly selected citizen who moved in 2004 was a person who moved to a different region to a different region.

Equation of the horizontal line that passes through the point (-5,1)

If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error a. will not change. b. will increase. c. will also increase from .01 to .05. d. will decrease.

Graph or explain how to graph the equation: y = 3x -5

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