A survey recently reported that the mean national annual expenditure for inpatient and outpatient services of all persons over 64 years of age was $5,423 with a standard deviation of $979. A random sample of 352 persons over age 64 living in Sudbury had an average expense of $5,516. We want to test whether the mean inpatient and outpatient expense of all Sudbury residents over age 64 is higher than the national average of $5,423. Calculate the P-value for this test.

Answers

Answer 1

Using the z-distribution, it is found that the p-value for this test is of 0.0375.

At the null hypothesis, it is tested if the expenses are the same as the national average, that is, of $5,423. Hence:

[tex]H_0: \mu = 5423[/tex]

At the alternative hypothesis, it is tested if it is higher, hence:

[tex]H_1: \mu > 5423[/tex]

We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

The parameters are:

[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.

For this problem, the values of the parameters are: [tex]\overline{x} = 5516, \mu = 5423, \sigma = 979, n = 352[/tex]

The value of the test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{5516 - 5423}{\frac{979}{\sqrt{352}}}[/tex]

[tex]z = 1.78[/tex]

The p-value is the probability of finding a sample mean above $5,516, which is 1 subtracted by the p-value of z = 1.78.

Looking at the z-table, z = 1.78 has a p-value of 0.9625.

1 - 0.9625 = 0.0375

Hence, the p-value for this test is of 0.0375.

A similar problem is given at https://brainly.com/question/25549474


Related Questions

please help me calculation completing square?
x²+2x-24=0?​

Answers

Answer:

x = 4, -6

Step-by-step explanation:

x = 4, -6

g A long-term study has revealed that a test for cancer in men is very effective. The study shows that 89% of the men for which the test is positive actually have cancer. If a man selected at random tests positive for cancer with this test, what is the probability that he does not have cancer

Answers

The answer is 89% because I had that Same question and it was 89%

Find the domain of the function.



f(x) = -5x + 3

Answers

Enter a problem...

Calculus Examples

Popular Problems Calculus Find the Domain and Range f(x)=5x-3

f

(

x

)

=

5

x

3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

(

,

)

Set-Builder Notation:

{

x

|

x

R

}

The range is the set of all valid

y

values. Use the graph to find the range.

Interval Notation:

(

,

)

Set-Builder Notation:

{

y

|

y

R

}

Determine the domain and range.

Domain:

(

,

)

,

{

x

|

x

R

}

Range:

(

,

)

,

{

y

|

y

R

}

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=21(0.97)^x
what is the % increase

Answers

Answer:

Step-by-step explanation:

As the number under the exponent is less than 1, this is a decay function.

y decreases by (1 - 0.97)100 = 3% for each unit increase in x

so the increase would be -3%

What is 11% of 96 students

Answers

Answer:

8.7

Step-by-step explanation:

8.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.7

Suppose `h\left(t\right)=-5t^{2}+10t+3`is an expression giving the height of a diver above the water (in meters), t seconds after the diver leaves the springboard.



a. How high above the water is the springboard? Explain how you know.

Answers

Answer:

Step-by-step explanation:

a) The height of the springboard above the water should be h(0) : Read, the height at t = 0

h(0) = -5(0) + 10(0) + 3

h(0) = 0 + 0 + 3

h(0) = 3

a) 3 meters

b)  The time it takes the diver to hit water should be, the positive 0 solution for t.  Remember, in a quadratic equation,  there are two values for t where a parabola crosses the horizontal axis, which in this case would be t.  Just by looking at the function, h(t) = -5t2 + 10t + 3 , one should be able to see that it cannot be factored easily, so it requires the Quadratic Formula to find the zeros ; x = -b ±√(b2-4ac)  / 2a

Substitute t for x, and use the coefficients for a, b, c:

t  =  (-10 ± √((102 - 4(-5)(3)))/2(-5)

t = (-10 ±√(100 + 60))/-10

t = (-10 ±√160)/-10) ; Now factor the 160 to simplify:

t = (-10 ±√(10*16))/-10

t = (-10 ±4√10)/-10 ; Factor out leading coefficient of -2 from the numerator:

t = -2(5 ± 2√10)/-10

t = (5 ± 2√10)/5

Using a calculator to find the zeros, and disregarding the negative zero (because t starts at 0):

t ≈ 2.265

b) approx. 2.265 seconds for diver to hit water.

c) To find this, set the function equal to 3 to find what other value for t would be equal to 3 (we know one is 0).

-5tt + 10t + 3 = 3

-5t2 + 10t = 0 ; factor out t

t(-5t + 10) = 0

We know t = 0:

We also know that -5t + 10 = 0

-5t = -10

t = 2

c) 2 seconds. This is the time that diver would equal height of t=0 which is where he started, and where he equals the height of the springboard.

d and e) The peak of the dive (parabola), is determined using the formula h = -b/2a (Derived from the Quadratic Formula) to find the y value (in this case, the h value, answering e) and then using that result in the function to find the x value (in this case, the t value answering d) of the point where the parabola (dive path) reaches a maximum(height), or minimum(in upward opening parabolas).

h = -10/2(-5)

h = -10/-10

h = 1

h(1) = -5(1)2 + 10(1) + 3

h(1) = -5 + 10 + 3

h(1) = 8

d) At t = 1 second, diver will have reached peak of dive.

e) At t = 1 second, diver will have reached a maximum height of 8 meters.

A man earned £6500 for the month. He paid 2/5 in tax . How much did he have left to spend?

Answers

Answer:

$2600

Step-by-step explanation:

Im not too fond of the conversion of Pounds and USD. But if it were USD 2/5 of the amount would be $2600

what is the probability of a person randomly selecting an apple pie, eating it, then selecting another apple pie

Answers

Answer:

if its me then i will bye the store. but the answer is 50%

Step-by-step explanation:

Please take a look at the picture

Answers

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {C.\:None\:of\:the\:above.}}}}}}[/tex] ✔

[tex]\:\large{\boxed{\frak{ Step-by-step\:explanation: }}}[/tex]

A. [tex]x - ( - x) = -x[/tex]

Let us first solve for L. H. S.

We have,

[tex]x - ( - x)[/tex]

[tex] = x + x[/tex]

[tex] = 2x[/tex]

[tex]≠ - x[/tex]

[tex]≠ R. H. S. [/tex]

Hence, option A is incorrect.

B. [tex]0 - ( - x) = - x[/tex]

Solving for L.H.S. , we have

[tex] = 0 - ( - x)[/tex]

[tex] = + x[/tex]

[tex]≠ - x[/tex]

[tex]≠ R. H. S. [/tex]

Hence, option B is ruled out too.

Therefore, the correct answer is [tex]\sf\red{ option\:C}[/tex].

x-10/3=5x+2/2 I need help with he next step please

Answers

Answer:

x2 the left side and x3 the right side of the equation

Answer:

X = -2

First you cross multiply, and then you expand to get 15x+6

after that its basic algebra with adding/subtracting from each side, simplifying, and then divide both sides by -13.

Write an inequality to show: The population of China (p) is at least 1,000,000,000 people.
I'll try to mark brainiest

Answers

Answer:

p ≥ 1,000,000,000

Step-by-step explanation:

since it says "at-least" that is implying that, that is the estimate and there is most likely more people and it is not exactly 1,000,000,000 so we need to use ≥ to show that it could be greater than or equal to 1,000,000,000.

plz help on a timed test will pay 10 points and make brainlest

What other countries have set up early earthquake warning systems? Which of these countries are in the Ring of Fire? Why is it important for these Ring of Fire countries to have warning systems?

Answers

Answer:

Mexico, Japan, South Korea, Taiwan, and the United States, Chile, Japan, the US west coast;  Chile, Japan, the US west coast; So all that is left for the people who live around the Ring of Fire is to be aware of the danger, perhaps to live further inland, build safer, earthquake-resistant housing, and for nations everywhere to improve oceanic and land-based early-warning systems to help minimize the risk to life

Step-by-step explanation:

help me please the drop down menu is the same for top and bottom i’m lost:(

Answers

I think…

0=2 : no solutions
2=2 : infinite solutions

Answer:

1) No solution

2) Infinitely many solutions

Step-by-step explanation:

1) No solution

0=2 is false.

2) Infinitely many solutions

2=2 is true because both sides are equal, hence, it is an infinite solution.

Hope this helps :)

Help please please need quick

Answers

14 times 14=196
7 times 7= 49
196-49=147
The length of X is approximately 7 root 3. Or 12.12 as a decimal

2/3x + 7 = -1/5x + 3

Answers

if there is any doubt leave a comment

Soraya earned $40 in October. She earned $50 in
November.
What is the percent increase or decrease in Soraya's monthly earnings?
A. 15% decrease
B. 30% increase
C. 25% increase
D. 20% decrease

Answers

25% increase.

Explanation: 25% of $40 is $10. You add $10 to $40 you get $50.

Expand the function.
f(x) = (2x + 3)4

Answers

Answer:

y = 8x + 12

Step-by-step explanation:

y = (2x + 3)4

Distribute the 4 to the 2x  and 3

y = 8x + 12

^ Expanded form

see question above ^^​

Answers

I think the answer is (4) because if you rotate AEC to the left (counterclockwise) and follow by the scale factor of 2 so, CE = 4x2 = 8 and CA = 3x2 = 6. Hope this help :))

A punch recipe requires 2 cups of cranberry juice to make 4 gallons of punch. Using the same recipe, what is the amount of cranberry juice needed for 12 gallon of punch

Answers

Answer:

we need 6 cups of cranberry juice for 12 gallons of punch

Please take a look at the picture

Answers

Answer:

D) The number that is 5 to the right of -6 on the number line

Hope this helps :)

2yx= 4 is it a linear function?

Answers

Answer:

No, it is not a linear function, rather a rational function

Step-by-step explanation:

Because the term on the left-hand side contains both x and y, then neither variable varies directly with the other, hence, it's a rational function:

2yx=4

yx=2

y=2/x

how to find the volume of an oven with the inside dimensions 3 ft by 1.5 ft by 3 ft

Answers

9514 1404 393

Answer:

  13.5 ft³

Step-by-step explanation:

The volume of a cuboid is the product of its length, width, and height:

  V = (3 ft)(1.5 ft)(3 ft) = 13.5 ft³

The volume of the oven is 13.5 ft³.

__

You may see this as the formula ...

  V = LWH

Answer: 3x10^2 mi

example:

Answers

Answer:

3000

Step-by-step explanation:

Answer:

300

Step-by-3step explanation:

Hey everyone! Can you help me out with this(for those wondering, these are test corrections, I plan to do half today and half tomorrow)

State whether the following relation is a function.​

Answers

Answer:

no its not since some dots are above each other and fail the vertical line test

Hope This Helps!!!

Answer:

no the x value repeat

Step-by-step explanation:

Find the accumulated value of an investment of $2000 at 8% compounded continuously for 4 years

Answers

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &4 \end{cases} \\\\\\ A=2000e^{0.08\cdot 4}\implies A=2000e^{0.32}\implies \boxed{A\approx 2754.26}[/tex]

a car travels 55 miles per hour for 2 hours. How far did it travel in 1 1/2 hours

Answers

Answer:

82.5 miles in 1 1/2 hours

Step-by-step explanation:

Using the information the question gives us we can find the appropriate answer to this question by dividing the miles per hour by two, and then add that number to the additional miles per hour.

55 miles = one hour

2 hours = 110 miles

1 1/2 hours = 55 ÷ 2 = 27.5

55 + 27.5 = 82.5 miles

82.5 miles

Hope this helps

What are 5 rules to follow in a science lab?

Answers

Answer:

Step-by-step explanation:

1. Wear safety glasses

2. Be accompanied by an adult

3. Wear proper lab clothing

4. Alert Lab instructor if an accident were to happen

5. Follow all instructions given by lab instructor

The length of a rectangle is three times its width. if the area of the rectangle is 75 in2, find its perimeter.

Answers

Answer:

  40 in

Step-by-step explanation:

For a width of w, the length is 3w and the area and perimeter are ...

  A = LW = (3w)(w) = 3w^2

  P = 2(L+W) = 2(3w +w) = 8w

We are given the area, so we can find w to be ...

  75 in^2 = 3w^2

  25 in^2 = w^2 . . . . . divide by 3

  5 in = w . . . . . . . . . square root

Then the perimeter is ...

  P = 8w = 8(5 in) = 40 in

a man walks for 45 minutes at a rate of 3 mi/h then jogs for 75 minutes at a rate of 5 mi/h then rests for 30 minutes and finally walks for 90 minutes at a rate of 3 mi/h. Write a piecewise-defined function expressing the distance he traveled as a function of time.

Answers

Answer:

Sorry need points

Step-by-step explanation:

Gven: f(x) = 4x +1 and (x)= x^2 + 1.

find (fog)(x)​

Answers

Answer:

Step-by-step explanation:

27836?+_68_729+_8978

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