The lengths of time (in years) it took a random sample of 32 former smokers to quit smoking permanently are listed.

11.8 14.4 10.8 10.4 16.2 20.5 12.6 10.4 19.5 14.2 12.8 17.6 15.9 21.2 18.4 22.9 7.9 11.4 9.5 17.2 14.5 21.7 16.8 12.9 8.9 16.3 21.3 13.6 17.4 13.7 7.8 19.8

Assume the population standard deviation is 6.6 years. At α=0.09, is there enough evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 14 years? Complete parts (a) through (e).

(a) Identify the claim and state the null hypothesis and alternative hypothesis.
(b) Identify the standardized test statistic. Use technology. ​
(c) Find the​ P-value. Use technology.
(d) Decide whether to reject or fail to reject the null hypothesis and​
(e) interpret the decision in the context of the original claim at the 10 ​% level of significance.

Answers

Answer 1

a. The null hypothesis is H₀: μ = 14 and alternative hypothesis is Ha: μ ≠ 14

b. The t-test for the data is 1.11

c. The p-value for the t-test is 0.28

d. We accept the null hypothesis since the p-value is greater than the significance value.

e. The decision to fail to reject the null hypothesis means that we do not have enough evidence to support the claim

What is the null and alternative hypothesis?

(a) The claim is that the mean time it takes smokers to quit smoking permanently is 14 years.

Null hypothesis (H₀): The mean time it takes smokers to quit smoking permanently is 14 years.

H₀: μ = 14

Alternative hypothesis (Ha): The mean time it takes smokers to quit smoking permanently is not 14 years.

Ha: μ ≠ 14

(b) To identify the standardized test statistic, we can use the formula:

t = (x - μ) / (s / √n)

where:

x is the sample mean,

μ is the population mean,

s is the population standard deviation,

n is the sample size.

Given:

Sample mean (x) = 15.29375 (rounded to 5 decimal places)

Population mean (μ) = 14

Population standard deviation (s) = 6.6

Sample size (n) = 32

Using these values, we can calculate the standardized test statistic.

t = (15.29375 - 14) / (6.6 / √32)

t = 1.11

(c) To find the p-value, we need to use the t-distribution table or statistical software. Since using technology is mentioned in the question, we will use it to calculate the p-value.

The p-value for a two-tailed test is approximately 0.28.

(d) We compare the p-value to the significance level α = 0.09.

Since the p-value 0.28 is greater than the significance level (0.09), we fail to reject the null hypothesis.

(e) The decision to fail to reject the null hypothesis means that we do not have enough evidence to support the claim that the mean time it takes smokers to quit smoking permanently is different from 14 years at the 10% level of significance.

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Related Questions

PLSSSS HELPPPP PLSSSS PLS HELPPPPP!!!!!!

Answers

Answer:

B -- (5 smoothings)(price of 1 smoothie) + tip = $23

Step-by-step explanation:

5 smoothies(price of 1 smoothie)+tip=23

What is the median of the data set? {5, 3, 4, 2, 6} Enter your answer in the box. Round to the nearest tenth.

The best answer will receive brainiest.

Answers

Answer:

4

Step-by-step explanation:

To find median, arrange the data set in ascending order. Then the middle term is the median

2 , 3 , 4 , 5 , 6

Median = 3rd term  = 4

Answer:

4 is the median

Step-by-step explanation:

From least to greatest:

2,3,4,5,6

Since the total values is odd, the middle number is the median

4 is the median

Help pls I’m on a time limit. Please and thank you <33

Answers

Answer: the answer is 3/10

Step-by-step explanation: because its 3/10

Answer:

es

3/ 10

Step-by-st

Please hurryyyyy !!!! What's the slope and y intercept of 4y = 2x - 12

Answers

Answer:

slop is 0.5 and intercept of y is -3

Answer:

½ is the slope,-3 is the intercept

Step-by-step explanation:

now to find the slope and intercept

we use the equation,

y=mx + c

where m is the slope

and c is the y intercept

so we compare 4y=2x-12 to the equation

but we first have to make y the subject of the equation in the question – 4y is already the subject –

y=2x-12/4

y=2x/4 -3

comparing...

we see that m is 2/4=½ c= -3

In desperate need of help. If anyone could help it would be greatly appreciate. Will rate brainliest!

Answers

Answer:

7 people

Step-by-step explanation:

Chocolate: 350 / 100 = 3.5 x 2 = 7

Butter: 45 / 10 = 4.5 x 2 = 9

Eggs: 8 / 2 = 4 x 2 = 8

The amount of chocolate is the limiting factor as you have enough eggs for 8 people and enough butter for 9 people, but only enough chocolate for 7 people

Can i pass 7th grade with 3 Fs?

Answers

Answer:

Depends on the state you’re from

Step-by-step explanation:

Answer:

Yes you can! Grades from middle school don't matter when you get to high school. But try to get those grades up!

Find the cross product a x b where a = (3, -3, -2) and b = (3,-1,-2). ахь Find the cross product cx d where c = (1, -2,-2) and d=(-5,3,-1).

Answers

The cross product of vector c and d is equal to (-4,9,13).

The cross product of two vectors a and b in three-dimensional space is a vector that is perpendicular to both a and b and thus normal to the plane containing them. Here, we have to find the cross product of two given vectors. The given vectors are:a = (3, -3, -2) and b = (3, -1, -2)  So, a x b = (4,0,6).The second one is given as: c = (1, -2,-2) and d=(-5,3,-1).

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

In mathematics, a vector's magnitude is defined as the length of a segment of a directed line, and the vector's direction is indicated by the angle at which the vector is inclined.

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We know the following about the transformation A:
A ï1 0 ò=ï2 0 ò
and A ï0 1 ò=ï1 1 ò
73.1 Draw C2 and A(C2), the image of the unit square under A.
73.2 Compute the area of A(C2).
73.3 Compute det(A).

Answers

73.1 A(C2) is a quadrilateral with vertices (0, 0), (1, 0), (1, 2), and (0, 2).

73.2 The area of A(C2) is 2.

73.3 The determinant of A is 0

To draw C2 and A(C2),  to understand the transformation A and to the unit square.

Given the information:

A:

| 1 0 |

| 2 0 |

A maps the vector [1, 0] to [2, 0], and it maps the vector [0, 1] to [1, 1]. This provides us with the information to draw C2 and A(C2).

73.1 Draw C2 and A(C2):

C2 represents the unit square with vertices (0, 0), (1, 0), (1, 1), and (0, 1).

To draw A(C2), the transformation A to each vertex of C2 and connect the transformed vertices to form the image of C2 under A.

Applying A to the vertices of C2:

A(0, 0) = (1 × 0, 2 × 0) = (0, 0)

A(1, 0) = (1 × 1, 2 × 0) = (1, 0)

A(1, 1) = (1 × 1, 2 × 1) = (1, 2)

A(0, 1) = (1 × 0, 2 × 1) = (0, 2)

Connecting the transformed vertices, we get the image of C2 under A:

73.2 Compute the area of A(C2):

To compute the area of A(C2),  divide it into two triangles and calculate their areas separately.

Triangle 1: (0, 0), (1, 0), (1, 2)

Base of Triangle 1 = 1 - 0 = 1

Height of Triangle 1 = 2 - 0 = 2

Area of Triangle 1 = (1/2) × Base × Height = (1/2) × 1× 2 = 1

Triangle 2: (0, 0), (0, 2), (1, 2)

Base of Triangle 2 = 1 - 0 = 1

Height of Triangle 2 = 2 - 0 = 2

Area of Triangle 2 = (1/2) × Base × Height = (1/2) × 1 × 2 = 1

Total Area of A(C2) = Area of Triangle 1 + Area of Triangle 2 = 1 + 1 = 2

73.3 Compute det(A):

To compute the determinant of A (denoted as det(A)), use the formula for a 2x2 matrix.

A:

| 1 0 |

| 2 0 |

det(A) = (1 ×0) - (0 × 2) = 0 - 0 = 0

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Tina drew a triangle with side lengths 6, 8, and 14. She claims it is a right triangle. Is she correct?

Answers

Answer:

No such a triangle can not exist.  

Can someone help me with this. Will Mark brainliest. Need answer and explanation/work. Thank you.

Answers

Answer:

Parallel: y = -2x + 2 (Or any value that isn't 4), Perpendicular: 1/2x + (Anything),

Neither: y = 4x - 7 (Or any random equation that does not have the same, or opposite reciprocal slope)

Step-by-step explanation:

How many real solutions exist for this system of equations? Y = -x + 1 y = -x2 + 4x − 2 A. Zero B. One C. Two D. Infinite

Answers

Answer:

Two solutions

Step-by-step explanation:

Given the functions Y = -x + 1 y = -x² + 4x − 2

Since they are both y values, we will equate them to have:

-x+1 = -x² + 4x − 2

Equate to zero

x²-x-4x+1+2=0

x²-5x+3 = 0

Since the resulting equation is quadratic (highest degree being 2), hence there will be two solutions to the equation

How many days in April

Answers

Answer:

There are 30 days according to the Georgian calender of the month of april.

Step-by-step explanation:

Can someone please help me with math

Answers

Answer:

A. 20.2 ft

Step-by-step explanation:

use the pythagorean theorem to get your answer.

a^2+b^2=c^2

17^2+11^2=c^2

289+121=410

***IMPORTANT, remember to square root the answer. 410 isn't your final answer, it's still in c^2 form. 20.2 is the correct answer after square rooting it. don't forget that for future problems

Answer:

A. 20.2 ft

Step-by-step explanation:

Hope it helps..

3/5 + 7/8 + 3/10
please help

Answers

Answer:

soln,

3/5+7/8+3/10

3×8/5×8+7×5/8×5+3×4/10×4

24/40+35/40+12/40

24+35+12/40

71/40

encontre as raízes quadradas dos números:
a)²√625​

Answers

25

porque al multiplicar 25×25 nos da 625

Answer:

25

Step-by-step explanation:

25x25=625

Use the following diagram to answer question 4 and 5
Exterior Angle Theorem
8.6 points
The measure of ZA is
Given the following diagram, find the measures of
LA and ZB
Type your answer...
B (2x + 4)
5
8.6 points
The measure of ZB is
Type your answer...
(3x - 13)
116°
А

Answers

Answer:

3x-13+2x+4=116( the sum of two interior angle is epual to the sum of exterior angle )

5x =116-9

5x=107

x=21.4 degree

then

angle a= 3*21.4-13

a=51.2degree

angle b=2*21.4+2

b =44.8degree

Step-by-step explanation:

plz make me brainliest

CORRECT ANSWER GETS BRAINLIEST
Explain how you would apply exponent rules to evaluate for the value of (x³/x)² if x =1/2?

Answers

Answer:

1/16

Step-by-step explanation:

Picture is attached. The quickest way is to simplify BEFORE plugging in x = 1/2

Mario tiene 4 pantalones de diferente color (azul, café, negro y blanco) y 6 camisas también de diferente color (blanca, negra, azul, café, gris y verde). Si Mario escoge una combinación al azar, ¿cuál es la probabilidad de que se vista con pantalón azul y camisa blanca?

Answers

1/15 es la posibilidad que existe

find the area of this polygon

Answers

Answer:

answer is 65 in²

hope this helps

¿Cuáles son los números primos entre 2 y 20?

Answers

Answer:

2 3 5 7

Step-by-step explanation:

A rectangular prism has a base perimeter of 28 inches and a height of 6 inches. What is the lateral surface area of the prism?​

Answers

Answer:

uhuhuhuhuhuhuhuhuhuhuh oh yeah

Step-by-step explanation:

Methods to rid a model of multicollinearity include:

Answers

Methods to rid a model of multicollinearity include:  Include determination,Collection of data,Variable change,Regression ridge

Multicollinearity in a model can be addressed in a number of ways, including:

Include determination: Eliminating at least one connected factors can assist with mitigating multicollinearity. Stepwise regression or LASSO regression can be used to select the most important features by analyzing the correlation matrix.

Collection of data: By introducing variation in the predictors, more diverse and independent data can help reduce multicollinearity. Expanding test size can likewise help in relieving multicollinearity impacts.

Variable change: Multicollinearity can be reduced by transforming variables using centering, standardization, or power or logarithmic transformations. These changes change the scale or type of the factors, making them less associated.

Regression ridge: By adding a penalty term to the least squares estimation, ridge regression reduces the impact of multicollinearity and reduces the coefficients. This regularization method balances out the appraisals and works on model execution.

PCA, or Principal Component Analysis,: PCA can be used to generate uncorrelated linear combinations of the starting variables. These new factors, known as head parts, can be utilized as indicators in the model, successfully lessening multicollinearity.

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Simplify this expression

Answers

I think this would be 7st^6 u^8 v^4 because the other two terms cancel each other out.

Find the basis for the kernel and imagine of this transformation. Let T : P₂ → R where T(p(x)) = p(1). Find a or the kernel and image of this transformation.

Answers

The basis for Ker(T) is {}, and the basis for Im(T) is {1}.

Since, The kernel of T, denoted Ker(T), is the set of all elements in P₂ that are mapped to zero in R by T.

In other words, Ker(T) is the set of all polynomials in P₂ such that

T(p(x)) = p(1) = 0.

Hence, To find the kernel, we need to solve the equation p(1) = 0.

Since, The only polynomial that satisfies this condition is p(x) = 0.

Therefore, Ker(T) = {0}.

Now, the image of T.

The image of T is the set of all elements in R that are mapped to by some element in P₂ under T.

In other words, Im(T) is the set of all possible values of p(1) for all polynomials p(x) in P₂.

Some example: - If p(x) = 1 + 2x + x², then p(1) = 1 + 2 + 1 = 4.

So, we can see that Im(T) is the set of all real numbers.

Hence, the basis for the kernel and image of T.

Since Ker(T) = {0}, the basis for the kernel is the empty set, denoted by {}.

Since Im(T) is the set of all real numbers, any non-zero real number can be expressed as a scalar multiple of any other non-zero real number.

Therefore, the basis for Ker(T) is {}, and the basis for Im(T) is {1}.

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Saul decides to use the IQR to measure the spread of the data. Saul calculates the IQR of the data set to be . Saul asks Jasmine to check his work. Saul copies the data in numerical order from least to greatest for Jasmine.

Answers

The question is incomplete. The compete question is :

Saul decides to use the IQR to measure the spread of data. Saul calculates the IQR of the data set to be 27. Saul asks Jasmine to check his work. Saul copies the data in numerical order from least to greatest for Jasmine. 25, 30, 50, 50, 50, 50, 56, n, 250. What is the value of n that will make the IQR of the data set equal to 27?

Solution :

The inter quartile range is being measured as : 3rd quartile - 1st quartile

The 1st quartile = 25% mark

The 3rd quartile = 75% mark

The data set as given in the question is :

25, 30, 50, 50, 50, 50, 56, n, 250

Therefore, the total number of the sample = 9

And the median is = 50

The median separates the given data sets into two equal halves-- that is the upper half and the lower half.

Let the middle of a lower half is the 1st quartile be [tex]$Q_1$[/tex]

And the middle of a 2nd half is the 3rd quartile be [tex]$Q_3$[/tex]

∴ [tex]$Q_1=\frac{30+50}{2}$[/tex]

        [tex]$=40$[/tex]

  [tex]$Q_3=\frac{56+n}{2}$[/tex]

Now for the IQR of the data set to be equal to [tex]$27$[/tex],

[tex]$\frac{56+n}{2}-40=27$[/tex]

[tex]$\frac{56+n}{2}=27+40$[/tex]

[tex]$\frac{56+n}{2}=67$[/tex]

[tex]$56 +n=134$[/tex]

[tex]$n=134-56$[/tex]

[tex]$n=78$[/tex]

Use the box method to distribute and simplify (2 + 1)(2x - 3). Drag and drop the
terms to the correct locations of the table.

Answers

Answer:

2x^2-x-3

(2x)(-3)

(x)

(1)

Step-by-step explanation:

Distribute

(2x^2) (-3x)

(2x) (-3)

Im giving brainliest

Answers

Answer:

√17 - 3   >   -2 + √5

A password is required to log into a system that only recognizes numbers and letters of the alphabet (not case sensitive). You want to create a password using 5 numbers or letters, but cannot reuse any of them. How many different passwords are possible?

Answers

There are 60,466,176 possible passwords for a system that acknowledges both digits and letters of the alphabet (and does not differentiate between uppercase and lowercase letters) and requires a 5-character password with no repeated characters.

For the purpose of computing the total number of possible passwords, it is necessary to take into account the number of options available for each character position. Within the constraints of the system, there are 10 different options for each number (0-9) and 26 different options for each letter (A-Z).

There are a total of 36 options available to us when it comes to the first character position (26 letters and 10 numerals). We are left with 35 options for the second place because we are unable to recycle any of the characters (36 options, minus the one that has already been used). In a similar fashion, we have 34 options for the third position, 33 options for the fourth position, and 32 options for the fifth position.

To calculate the total number of possible passwords, we multiply the number of choices for each position together: 36 * 35 * 34 * 33 * 32 = 60,466,176. Given the parameters of this system, there are consequently sixty-four million, four hundred sixty-six thousand, one hundred seventy-seven different passwords that might be used.

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find the value of x for both problems.​

Answers

Answer:

Step-by-step explanation:

In Problem 6, 3/x = tan 30 degrees, or x/3 = 1 / (tan 30 degrees), or

x =   3 / (tan 30 degrees).  Using a calculator:  x = 3 / (0.449) = 6.68 units

In Problem 9, we begin by finding the length of the hypotenuse of the upper triangle:  sin 60 degrees = 9√3 / hypotenuse, or

hypotenuse = 9√3/ (√3 / 2) = 9/2.  Then the hypotenuse of the 45-45-90 triangle is 9/2.  Thus, cos 45 degrees = x / (9/2), or

2x      √3

---- = -------

 9        2

                                                                                    9√3

Cross-multiplying, we get 4x = 9√3, so that x = -------------

                                                                                        4

Kai's mom gave him $25 to spend at the book fair. Kai wants to buy as many books as he can. The
cost of each book is $3. He also wants to buy one poster for $2. Write an inequality to show how
many books he can buy. Highlight your inequality in green. Then,solve the inequality

Answers

Answer:

7 books

Step-by-step explanation:

i cant write it in an equaction but basically 25 - 2 = 23

then 3 x 7 = 21 so he can only buy 7 books and he'll have 2 dollars left

3x + 2 = 25. x= 7

3x +2 =25
-2 -2
23
3x = 23


23 divided by 3 = 7
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