a researcher wishes to test the claim that the average age of lifeguards in ocean city is greater than 24 years. she selects a sample of 36 lifeguards and finds the mean age of the sample to be 24.7 years. from past data, she knows the population standard deviation is years. is there evidence to support the claim at a 5% level of significance?

Answers

Answer 1

The average age of lifeguards in Ocean City is significantly greater than 24 years at a 5% level of significance.

What is Standard deviation?

Standard deviation is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

To determine whether there is evidence to support the claim that the average age of lifeguards in Ocean City is greater than 24 years at a 5% level of significance, we need to perform a one-tailed t-test. A one-tailed t-test is used to test whether the mean of a sample is significantly greater than (or less than) a certain value.

To perform the t-test, we first need to calculate the t-statistic, which is defined as:

      [tex]t = (mean - null value) / (standard error / \sqrt{n} )[/tex]

where mean is the mean age of the sample of lifeguards, null value is the value that the null hypothesis is testing against (in this case, 24 years), standard error is the standard error of the mean age, and n is the number of lifeguards in the sample.

Plugging in the values from the problem, we get:

           [tex]t = (24.7 - 24) / (standard \ error / \sqrt{36} )\\\\= 0.7 / (standard\ error / 6)[/tex]

The standard error of the mean is a measure of the variability of the sample mean, and is calculated as:

   [tex]standard \ error = population \ standard\ deviation / \sqrt{(n)}[/tex]

Plugging in the values from the problem, we get:

standard error = / sqrt(36) = / 6 =

Substituting this value back into our expression for t, we get:

    t = 0.7 / ( 6)

      = 1.8

For a one-tailed t-test at a 5% level of significance, the critical value is 1.645. This means that if the t-statistic is greater than 1.645, we can reject the null hypothesis and conclude that there is evidence to support the claim.

So we can reject the null hypothesis and conclude that there is evidence to support the claim that the average age of lifeguards in Ocean City is significantly greater than 24 years at a 5% level of significance.

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Related Questions

Easy questions just a bit of help no rush 100 points to do this

Answers

Is this a test or do you need help

Spider Rock is located in Canyon de Chelly National Park in Arizona. A surveyor stands 370 feet from the base of Spider Rock. From a point 5.5 feet above the ground, he measures the angle of elevation to the top of Spider Rock to be 65°. According to the surveyor's measurements, what is the height of Spider Rock? Round your answer to the nearest tenth. A. 178.0 ft. B. 340.8 ft. C. 413.7 ft. D. 799.0 ft.

Answers

Answer:

799 feet

Step-by-step explanation:

We solve using the Trigonometric function of Tangent.

tan theta = Opposite /Adjacent

From the above question, we have the height of the surveyor = 5.5 feet

theta = Angle of elevation = 65°

Adjacent = 370 feet

Let Opposite = height + height of spider rock

tan 65° = h - 5.5 /370 feet

Cross Multiply

tan 65° × 370 feet = h - 5.5

793.46756059 feet = h - 5.5

h = 793.46756059 feet + 5.5

h = 798.96756059 feet

Approximately = 799 feet

The height of the Spider rock = 799 feet

Calculate the product below and give your answer in scientific notation.
(1.3 x 10-^2) (0.05) = ?

Answers

Answer:

1 Simplify 1.3\times 101.3×10 to 1313.

(13-2)\times 0.05

(13−2)×0.05

2 Simplify 13-213−2 to 1111.

11\times 0.05

11×0.05

3 Simplify.

0.55

0.55

The product of  (1.3 x 10⁻²) and (0.05)  is 0.065x 10⁻²

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

We need to find the product of (1.3 x 10⁻²) and (0.05)

Multiplication is a method of finding the product of two or more numbers

First multiply as if there is no decimal.

Next, count the number of digits after the decimal in each factor.

Finally, put the same number of digits behind the decimal in the product.

1.3×0.05=0.065

So 0.065x 10⁻² is the value of product (1.3 x 10⁻²) and (0.05)

Hence, the product of  (1.3 x 10⁻²) and (0.05)  is 0.065x 10⁻²

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In ΔQRS, the measure of ∠S=90°, QR = 7.7 feet, and SQ = 6.5 feet. Find the measure of ∠R to the nearest tenth of a degree.

Answers

Answer:

57.6°

Step-by-step explanation:

It is always helpful to draw a picture.  Also, you need to memorize all the definitions of the trig functions.  For example,

sine of an angle = opposite side/hypotenuse

In your case, SQ is opposite side to angle R and QR is the hypotenuse

Therefore, sin R = 6.5/7.7

          m∠R =  arcsin (6.5/7.7) = 57.6°

if f (x) = 8 (5x - 2) find f (x)​

Answers

Answer:

f-1(x) = (x - 16)/40

B

Step-by-step explanation:

Call f(x) = y

Interchange x and y

x = (5y + 2)*8             Remove the brackets

x = 40y + 16               Subtract 16 from both sides

x - 16 = 40y                Interchange the left and right sides

40y = x - 16                Divide by 40

y = (x - 16)/40

f-1(x) = (x - 16)/40

find the missing side. round to the nearest tenth.

Answers

Answer:

A. 5.2

Step-by-step explanation:

I was taught how to do this using the SOH CAH TOA method.

Step 1: Circle your given angle.

Step 2: Label O, H, and A. The line across from your circled angle will be labeled O. The side across from the right angle is H. The last unmarked side is A.

Step 3: Cross off the useless side, in this case, that would be A because there is no corresponding information.

Step 4: Identify if it is sine, cosine, or tangent using SOH CAH TOA. In this case, you only have an O and H so we will use SOH.

Step 5: Set up the equation. The equation is [tex]\frac{sine(31)}{1} =\frac{x}{10}[/tex]. We will use sine of the given angle is equal to the side marked O over the side marked H.

Step 6: Solve for x until x is by itself, then enter into your calculator.

You will enter [tex]sine(31) * 10[/tex] into your calculator and round if necessary.

Carson can choose one vehicle (car or truck), one color (blue, red, or silver), and one type of transmission (standard or automatic). How many possible outcomes are there?

Answers

Answer:

12 possible outcomes

Step-by-step explanation:

Choosing 1 vehicle from 2 = 2C1 = 2

Choosing 1 color from 3 = 3C1 = 3

Choosing 1 type from 2 = 2C1 = 2

Number of possible outcomes :

2C1 * 3C1 * 2C1

2 * 3 * 2

= 12 different possible outcomes

A man wants to build around water fountain with diameter, d = 11.28 feet. The man is trying to put up a fence around the build with some wire. What is the length of the wire that the man needs to complete the task?


Answers

Answer:

35.44

Step-by-step explanation:

2 times pi times radius.

What is the slope of the line?

2
-2
1/2
1

Answers

Answer:

the answer to the question is 1

The answer is one, that’s the answer.

Melissa works at Best Buy and gets paid $250 a week plus
commission. She earns $15 for every cell phone she sales.
Which function can be used to find t, the amount of money
Melissa will receive on her weekly paycheck for selling n
number of cell phones?
A.
t=250x + 15
C. t = 15x
B.
t = 15x + 250
D. Not Here

Answers

Answer:

option b is correct

I hope it helps

3x+4y=25 x+5y=23
What does the variable of x and y represent in the system of equations

Answers

x= 1/27

Heart if it helps!

Point form : (3,4)
Equation form : x = 3 , y = 4

One pair of parallel sides proves a quadrilateral to be a parallelogram
True
False

Answers

False i don’t know if this is right
It has to be true because a quadrilateral has 4 sides and parallelogram and a set of parallel sides so I think it’s true

can someone help me with my perfect square homework? thank you.

Answers

Answer:

Any better explanation

Answer:

49

Step-by-step explanation:

Given

v² - 14v

To complete the square

add ( half the coefficient of the v- term )² to v² - 14v

v² - 14v + (- 7)²

= v² - 14v + 49

= (v - 7)² ← a perfect square

What is the probability that the spinner will not land on a 5 or 8? 5 points

Answers

Answer:

3/4

Step-by-step explanation:

Based on the spinner attached :

Faces are in equal divisions ; number of faces = 8

Probability the spinner will not land on a certain number = 1 - P(spinner lands on that number)

P(spinner lands on 5) = 1 /8

P(spinner will not land on 5) = 1 - 1/8 = 7/8

P(spinner lands on 8) = 1/8

P(spinner will not land on 8) = 1 - 1/8 = 7/8

Hence,

P(spinner will not land on 5 or 8)

Required outcome = (1, 2, 3, 4, 6, 7) = 6

Total possible outcomes = (1.2, 3, 4, 5, 6, 7, 8) = 8

P(spinner will not land on 5 or 8). = 6/8 = 3/4

The measures of three of the interior angles of a quadrilateral are 60o, 110o, and 90o What is the measure of the fourth angle of this quadrilateral?

Answers

Answer:

100 degrees

Step-by-step explanation:

sum of angles in a quadrilateral = 360

missing angle = 360 - (60 + 110 + 90) = 100

mo played 30 games of chess he won 18 of these games what fraction of the games did he win give your answer in its simplest form

Answers

Answer:

18/30

Step-by-step explanation:

Need help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Option J is the correct answer to your question.

State if the three numbers can be the measures of the sides of a triangle.
5, 12, 10
Yes or No

Answers

Answer:

yes

Step-by-step explanation:

Solve the right triangle shown in the figure, given the following measures. Remember, exact lengths can be approximated on a calculator. For example, StartRoot 2 EndRoot almost-equals 1.414. Angle A = 45 degrees, side A B = 12 StartRoot 2 EndRoot centimeters, Angle C = 90 degrees a. Side B C = 6 StartRoot 3 EndRoot centimeters, angle B = 45 degrees, Side A C = 6 StartRoot 3 EndRoot centimeters b. Side B C = 6 StartRoot 2 EndRoot centimeters, angle B = 45 degrees, Side A C = 6 StartRoot 2 EndRoot centimeters c. Side B C = 24 centimeters, angle B = 45 degrees, Side A C = 24 centimeters

Answers

Answer:

D. BC = 12cm, <B = 45, AC = 12cm

Step-by-step explanation:

Edge 2021

The measures of the lengths and angles are: BC = 12cm, <B = 45, AC = 12cm

What are right triangles?

A right triangle is a triangle that has one of its angle measure to be 90 degrees.

From the question, we have:

Angle B = 45 degrees

Since angle B is 45 degrees, then the legs of the triangle are equal (i.e. 12 cm)

Hence, the measures of the lengths and angles are: BC = 12cm, <B = 45, AC = 12cm

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HELP! I'LL MARK YOU BRAINLIST

Answers

Step-by-step explanation:

are in the solution:

(3,1)

(-1,2)

(6,0)

(0,0)

are not

(-2,-1)

(0,-4)

» What is the area of this trapezoid?

Remember to include in. Or in^2

Answers

Answer:

20 Inches

Step-by-step explanation:

Ok here is how you do it so the formula for a trapezoid is base 1 plus base 2 divided by 2 times the height. so, in this case the two bases are 2 in and 6 in so we add those together and get 8 then, we divided 8 by 2 and we get 4.

Then now, we multiply 4 and 5 for our height and get 20 inches.

PLEASE HELP ME!! I WILL GIVE BRAINLIEST. ITS DUE IN AN HOUR

Answers

Answer:

p-3=8.25

p=11.25

Answer:

p - 3 = 8.25 and 11.25

Step-by-step explanation:

hi there!

the question is asking us to first find out which equation we can use to solve this wordy problem.

its not going to be answers 1 or 3 since they are adding/ multiplying more on to our wooden plank, when the question is stating that we are subtracting 3 inches off.

knowing that now, our answer is p - 3 = 8.25 or 4 !

now all we have to do is add 3 to 8.25 to get our answer of how long the plank was before we cut it

3 + 8.25

= 11.25

p = 11.25 <---------------- our final answer!

i hope this helped you! i hope you have a good rest of your day :)

( im sorry if this this late!! )

How to find surface area of rectangular prism?

Answers

Answer:

.

Step-by-step explanation:

........

Sin(x)=sqrt3/2 solutions of

Answers

Answer:

pi/3+2pin, 2pi/3+2pi(n)

Answer:

the next one is c - pi/2

Step-by-step explanation:

A street light is 21 feet high and casts a 40-foot shadow. At the same time, a cell-phone
tower next to the street light casts a 57-foot shadow. Which proportion can be used to find
the height, H, of the cell-phone tower?

Answers

Answer:

21/H = 40/57

Step-by-step explanation:

Which of the following points are located 3 units from (-4,-2) ?

Answers

the units (-3,-1) and (-0,-0) are the following units located at (-4,-2).

write the expression in standard form
2x-(5+4x)

Answers

Answer:

- 2x - 5

Step-by-step explanation:

2x - (5 + 4x)

2x - 5 - 4x

- 2x - 5

Answer: The answer is -2x - 5

Step-by-step explanation:

Which rule defines S, for an = 3(0.7)n?

Sn=7(0.7n)

Sn = 2.1(0.7n)

Sn= 7(1-0.7n)

Sn= 2.1(1-0.7n)

Answers

Answer: C

Sn= 7(1-0.7n)

Step-by-step explanation:

The rule that defines S for [tex]a_n = 3(0.7)^n[/tex] is:

[tex]S_n = 7(1 - 0.7^n)[/tex]

The rule of S means that we calculate the rule that defines the sum of n terms of the geometric progression.

Given that:

[tex]a_n = 3(0.7)^n[/tex]

Rewrite as:

[tex]a_n = 3 (0.7)^n \times 1[/tex]

Replace 1 with 0.7/0.7

[tex]a_n = 3 (0.7)^n \times \frac{0.7}{0.7}[/tex]

Rewrite as:

[tex]a_n = 3 *0.7 \times \frac{(0.7)^n}{0.7}[/tex]

Apply law of indices

[tex]a_n = 3 \times 0.7 \times (0.7)^{n-1}[/tex]

[tex]a_n = 2.1 \times (0.7)^{n-1}[/tex]

The n term of a geometric progression is:

[tex]a_n = ar^{n-1}[/tex]

Compare [tex]a_n = ar^{n-1}[/tex] to [tex]a_n = 2.1 \times (0.7)^{n-1}[/tex]

[tex]a = 2.1[/tex] --- the first term

[tex]r = 0.7[/tex]

The sum of n terms of a geometric progression is:

[tex]S_n = \frac{a(1 - r^n)}{1 -r}[/tex]

This gives:

[tex]S_n = \frac{2.1(1 - 0.7^n)}{1 -0.7}[/tex]

[tex]S_n = \frac{2.1(1 - 0.7^n)}{0.3}[/tex]

[tex]S_n = 7(1 - 0.7^n)[/tex]

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-5x - 5 > 15 solve this inequality

Answers

Answer:

-5×-5>15

+5 +5

-5×>20

÷-5 ÷-5

x<-4

whe you divide by a negativr you flip the sign

The lines graphed below are perpendicular. The slope of the red line is 4.
What is the slope of the green line?

Answers

Answer: -1/4

Step-by-step explanation:

so lets just eliminate some of the choices here.

4 and -4 are 4/1 or -4/-1 and it doesnt go up or down 4 here so those can be ruled out. If we look at which way the green line is facing, positive goes up on the graph, but green line is going down so we can rule out 1/4. So all that is left is -1/4, so there's your slope.

b. -1/4 you can see two points (0,2) and (4,1) you can do rise over run or y2-y1/x2-x1 2-1/0-4= -1/4
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