The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing.
Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 66 11 19 96
EN 80 42 32 154
IS 54 30 31 115
ES 71 40 43 154
Column total 271 123 125 519
(a) Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance.
(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Answers

Answer 1

a)Using the chi-square distribution table, the critical value is 12.592 using Hypothesis.

b)The value of chi-square statistic for the sample is 16.042, given that

(a)Chi-square test

The Null Hypothesis H₀ : Myers-Briggs preference type is independent of area of study.

Alternative Hypothesis H₁ : Myers-Briggs preference type is dependent of area of study.

Test statistic is χ² = ∑ ((Oi - Ei)² / Ei)

Expected frequencies:To compute the expected frequencies of the data we use the formula:

Eij = (row total i * column total j) / n where

i is the row number and j is the column number.

To find the value of chi-square statistic, the following table is necessary:

Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 66 11 19 96
EN 80 42 32 154
IS 54 30 31 115
ES 71 40 43 154
Column total 271 123 125 519

We obtain the expected frequencies by the above formula, and these are listed in the table below.

Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 51.55 23.43 21.03 96
EN 86.71 39.56 27.73 154
IS 50.14 22.88 20.97 115
ES 82.61 37.13 32.27 154
Column total 271 123 125 519

The expected frequencies are computed by multiplying the row total and column total and dividing by the grand total, n.

Here, we have four rows and three columns.

Thus, the degrees of freedom are df = (4 - 1)(3 - 1) = 6 at the 0.05 level of significance.

Since we have four rows and three columns, the number of degrees of freedom will be 6.

Using the chi-square distribution table, the critical value is 12.592.

Since 16.04 > 12.592,

we reject the null hypothesis and conclude that Myers-Briggs preference type is dependent of area of study.

(b) Value of chi-square statisticThe formula to compute the chi-square statistic is

χ² = ∑ ((Oi - Ei)² / Ei) where Oi is the observed frequency and Ei is the expected frequency.

Calculating the chi-square statistic, we have

χ² = ((66 - 51.55)² / 51.55) + ((11 - 23.43)² / 23.43) + ... + ((43 - 32.27)² / 32.27)

  = 16.042 (rounded to three decimal places).

The value of chi-square statistic for the sample is 16.042.

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Related Questions

Warm-Up: Perpendicular Bisector
1.
What is WY? Explain your reasoning.

Answers

Answer: WY = 27

Step-by-step explanation:

Due to WX being a Perpendicular Bisector WY = WZ

4x - 5 = 2x + 11

Add 5 to both sides

4x = 2x + 16

Subtract 2x from both sides

2x = 16

Divide by 2

x = 8

So 4x - 5 of x = 8

4*8 = 32 - 5 =27

Answer:

27

Step-by-step explanation:

WY = WZ because XZ = XY

[tex]2x + 11 = 4x - 5\\(2x + 11) - 11 = (4x - 5) -11\\2x = 4x - 16\\-2x = -16\\x = 8\\\\WY = 4x - 5\\WY = 4(8) -5\\WY = 32 - 5\\WY = 27[/tex]

Can someone help me on this I’m struggling to figure it out...

Answers

Answer:

It's D

Step-by-step explanation:

While taking inventory at her pastry shop, Aisha realizes that she had 1/4 of a box of baking powder yesterday, but the supply is now down to 1/6 of a box. How much more baking powder did Aisha have yesterday?

Answers

Answer:

1/12

Step-by-step explanation:

[tex]\frac{1}{4} - \frac{1}{6}[/tex]

[tex]\frac{6 - 4}{24}[/tex]

[tex]\frac{2}{24}[/tex]

Converting to its simplest form, divide numerator and denominator by 2 = 1/12

Use one step of Euler's Method with Ar = .3 to approximate y(1.3) where y(x) is the solution of the differential equation y'(x) = 2xeª — y, with initial data y(1) = 0.

Answers

Using Euler's Method with a step size of 0.3 and the given initial data and differential equation, the approximate value of y(1.3) is 0.3 × 2[tex]e^{0.3[/tex].

To approximate the value of y(1.3) using Euler's Method, we need to take one step with a step size of h and update the y-value accordingly. Here's how to do it step by step:

Determine the step size, h. In this case, we want to approximate y(1.3) using the initial data at y(1). Since we know that x increases from 1 to 1.3, the step size is h = 1.3 - 1 = 0.3.

Calculate the slope at the initial point (x0, y0). The slope can be found using the given differential equation y'(x) = 2x[tex]e^a[/tex] - y. Plugging in the values x0 = 1 and y0 = 0, we get:

y'(1) = 2(1)[tex]e^{0.3[/tex] - 0 = 2[tex]e^{0.3[/tex].

Compute the approximate value of y at the next step. Using Euler's Method, we can update the y-value as follows:

y1 = y0 + h × y'(x0, y0)

= 0 + 0.3 × 2[tex]e^{0.3[/tex].

Evaluating the expression:

y1 = 0.3 × 2[tex]e^{0.3[/tex].

This gives us the approximate value of y(1.3) using Euler's Method with the given initial data and differential equation.

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For the given margin of error and confidence level, determine the sample size required. Show your answer in the integer form. You wish to estimate the proportion of shoppers that use credit cards. Obtain a sample size that will ensure a margin of error of at most 0.065 for a 92.5% confidence interval.

Answers

The sample size required to ensure a margin of error of at most 0.065 for a 92.5% confidence interval is 523.

To estimate the proportion of shoppers using credit cards with a desired margin of error and confidence level, determining the appropriate sample size is crucial.

In this scenario, we aim to achieve a margin of error of no more than 0.065 for a 92.5% confidence interval. The sample size required to fulfill these criteria is 523.

To comprehend the significance of these calculations, it's essential to understand the concepts of margin of error and confidence level. The margin of error represents the maximum amount of uncertainty we can tolerate in our estimate.

In this case, we want our estimate of the proportion of shoppers using credit cards to be accurate within ±0.065. A smaller margin of error indicates greater precision in our estimate.

The confidence level, on the other hand, reflects the level of certainty we have in the accuracy of our estimate.

A confidence level of 92.5% implies that if we were to repeat the sampling process numerous times, we would expect approximately 92.5% of the resulting confidence intervals to contain the true proportion of credit card-using shoppers.

The formula to calculate the sample size required for a proportion estimation is based on the desired margin of error, confidence level, and an assumed proportion (usually 0.5 for maximum variability).

This formula incorporates a z-value, which corresponds to the desired confidence level. For a 92.5% confidence level, the z-value is approximately 1.81.

By plugging the values into the formula and solving for the sample size, we find that a sample size of 523 is necessary to estimate the proportion of shoppers using credit cards with a margin of error no greater than 0.065 and a confidence level of 92.5%.

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As an avid cookies fan, you strive to only buy cookie brands that have a high number of chocolate chips in each cookie. Your minimum standard is to have cookies with more than 10 chocolate chips per cookie. After stocking up on cookies for the current Covid-related self-isolation, you want to test if a new brand of cookies holds up to this challenge. You take a sample of 15 cookies to test the claim that each cookie contains more than 10 chocolate chips. The average number of chocolate chips per cookie in the sample was 11.16 with a sample standard deviation of 1.04. You assume the distribution of the population is not highly skewed. Alternatively, you're interested in the actual p value for the hypothesis test. Using the previously calculated test statistic, what can you say about the range of the p value?

Answers

The test statistic is 1.09. The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. The range of the p-value is 0.1 to 1.

How to explain the information

If the p-value is less than 0.05, we reject the null hypothesis and conclude that the new brand of cookies has more than 10 chocolate chips per cookie.

If the p-value is greater than 0.05, we fail to reject the null hypothesis and cannot conclude that the new brand of cookies has more than 10 chocolate chips per cookie.

In this case, the p-value is between 0.1 and 1. Therefore, we cannot conclude that the new brand of cookies has more than 10 chocolate chips per cookie.

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What is the slope of a line perpendicular to the line whose equation is
3x + 3y = 45

Answers

Answer:

3(x+y)=45

x+y=15

y=-1x +15

so

slope(m) = -1

A car salesman sells cars with prices ranging from $5,000 to $45,000. The box plot shows the distribution of the numbers of cars he expects to sell over the next 10 years.

The salesman has observed that many students are looking for cars that cost less than $5,000. If he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years, how will the distribution be affected?

A. The mean and the median will be the same.
B. The median will shift to the right.
C. The mean will shift to the left.
D. The mean will shift to the right.

Answers

Answer:
I think is A

The longest run way at an airport has the shape of a rectangle and an area of 1,573,000 sq ft. This run way is 130 feet wide. How long is the run way?

Answers

Answer:

12,100 feet

Step-by-step explanation:

The longest run way at an airport has the shape of a rectangle and an area of 1,573,000 sq ft. This run way is 130 feet wide. How long is the run way?

The area of a rectangle = Length × Width

Width = 130 feet

Area = 1,573,000 sq ft

The Length = Area/Width

= 1,573,000 sq ft/130 feet

= 12,100 feet

Therefore, the runaway is 12,100 feet long.

if f(x) = 1/4x 1 and g(x) = 4(1/4x 1), what is the slope of the graph of g?

Answers

The slope of the graph of the function g(x) is 1, indicating that for every unit increase in x, the corresponding value of g(x) increases by 1.

To find the slope of the graph of the function g(x), we can use the power rule of differentiation. Let's differentiate g(x) step by step:

Step 1: Express g(x) in a simplified form.

g(x) = 4(1/4[tex]x^1[/tex])

Step 2: Simplify the expression.

g(x) = x

Step 3: Differentiate g(x) to find the slope.

The derivative of g(x) with respect to x is simply 1, as the derivative of x with respect to itself is 1.

Therefore, the slope of the graph of g(x) is 1.

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can someone dooo ittttttttt

Answers

Answer:

i dont know

Step-by-step explanation:

HELPPPPPPPPPPPPP meeeee please

Answers

Step-by-step explanation:

5. 4b = b + b + b + b (A)

4b = 2b + 2b (C)

6. 111 = 14a

a = 111/14

a = 7.92

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Assuming that the sample variances are continuous measurements, find the probability that a random sample of 30 observations, from a normal population with variance 92= 5, will have a sample variance of s2 that is a) greater than 7.338; b) between 2.766 and 7.883.

Answers

a) chi-square = (30-1) * 7.338 / 5 = 42.456 b) The probability of having a sample variance between 2.766 and 7.883 is the difference between the cumulative probabilities of chi-square2 and chi-square1.

Answer to the aforemention questions

To find the probability in both cases, we need to use the chi-square distribution with n-1 degrees of freedom, where n is the sample size.

a) To find the probability that the sample variance is greater than 7.338, we need to find the upper tail probability of the chi-square distribution.

The chi-square statistic is calculated as:

chi-square = (n-1) * s^2 / sigma^2

In this case, n = 30, s^2 = 7.338, and sigma^2 = 5.

chi-square = (30-1) * 7.338 / 5 = 42.456

b) To find the probability that the sample variance is between 2.766 and 7.883, we need to find the cumulative probability within that range.

First, we calculate the chi-square statistics for both values:

chi-square1 = (30-1) * 2.766 / 5 = 15.359

chi-square2 = (30-1) * 7.883 / 5 = 43.179

The probability of having a sample variance between 2.766 and 7.883 is the difference between the cumulative probabilities of chi-square2 and chi-square1.

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PLEASE HELP!


The blank of y in 17y is 17.



Its either term, variable or coefficient

Answers

The answer is Coefficient because a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression

In the term, 17y 17 is the coefficient of 17y.

What are coefficients and like terms?

A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.

Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.

The term 17y together is a variable, In 17y 'y' is also a variable.

In front of 'y' the constant number is 17 and it is called the coefficient of 'y'.

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A delivery company purchases a $20,000 van. The value of the van depreciates at a rate of 19% per year. How many years will it take before the van is worth half its original purchase price? Round to the nearest tenth of a year.

A 1.7 years
B 4.0 years
C 3.3 years

Answers

The answer is C because u need to find the prcentage first which is 19%of 20000 is 3800 to find the answer is u need to multiple 3800 with any answer given like 1.7 or 4.0 or 3.3....here u go the answer nearest 10000 is 3.3 year because half of its original price...

The distance between two cities on a map measure 3.71 inches. The scale on the map shows that 2 inches is equal to 50 miles. How many miles apart are the two cities

Answers

Answer:

92.75 miles

Step-by-step explanation:

3.71 / 2 = 1.855

1.855 * 50 miles = 92.75 miles

What is the mode of the data set? {102, 102, 100, 94, 102} Enter your answer in the box.

Answers

Answer:

102

Step-by-step explanation:

The mode is the number that appears the most in the data set. 102 appears 3 times while the others only once

Flow many years after the tree is planted does the model predict the tree will reach a height of 65 feet?

Answers

B

this is the answer

PLEASEEEEE HELP ME ON THIS

Answers

may not know the answer that well but try this called symbolab. Hope that could help you

find the slope. (no units needed)

Answers

Answer: 4/5

Step-by-step explanation: It is 8/10, but if you simplify it, it is 4/5.

Simplify each radical expression, if possible 3v/7-5^4v/7

Answers

Answer:

cannot be simplified

Step -by-step explanation:

[tex]3\sqrt{7} - 5\sqrt[4]{7} \\[/tex]

The indexes are not the same so the radicals cannot be combined.

cannot be simplified

Combine the like terms to create an equivalent expression for −4y−4+(−3)

Answers

Answer:

-4y - 7

Step-by-step explanation:

−4y−4+(−3)

-4y - 4 - 3

-4y - 7

Please help me in this!!!!!!

Answers

Answer:

Lower (or First) Quartile = 15

Step-by-step explanation:

Answer:

15 I think

Step-by-step explanation:

been a while since I did that but I think 15

Can someone help me please?

Answers

Answer: pull the upper right hand corner (of the smaller box) all the way to the upper right hand corner of the bigger box, then pull the upper left hand corner of the smaller box all the way over to the other side but leave two squares on the end, this gives you 18 boxes across the top which works since 2cm is three boxes. make sure each side of the square has 18 boxes and you’ll be good

Step-by-step explanation:

Please helppp I need this for a better grade

Answers

Answer:

Step-by-step explanation:

Cos(x)=18/44=0.41

x=65.85

Factor 8b^3 – 4b^2 a - 18b + 9a completely.

Answers

Answer:

85

Step-by-step explanation:

Answer:

(2b-a)x(2b-3)x(2b+3)

Step-by-step explanation:

67% of 200 please give me the answer

Answers

Answer: 134

(Hope this helped with whatever you needed it for <3)

Solve the problem. Use synthetic division and the remainder theorem to determine if [x−(3−2i)] is a factor of f(x)=x2−6x+13. Select one: a. No b. Yes

Answers

Using synthetic division and the remainder theorem, we can determine if [x−(3−2i)] is a factor of f(x)=x^2−6x+13.

To determine if [x−(3−2i)] is a factor of f(x)=x^2−6x+13, we can use synthetic division. First, we need to rewrite the given factor in the form x - c, where c is the conjugate of 3 - 2i, which is 3 + 2i.

Performing synthetic division with 3 + 2i as the divisor: f(x)=x^2−6x+13, we can use synthetic division. First, we need to rewrite the given factor in the form x - c, where c is the conjugate of 3 - 2i, which is 3 + 2i.

Performing synthetic division with 3 + 2i as the divisor:

 3 - 2i  |  1   -6   13

           __________________

           (remainder)

If the remainder is zero, then [x−(3−2i)] is a factor of f(x). However, if the remainder is nonzero, then [x−(3−2i)] is not a factor of f(x). Therefore, based on the result of the synthetic division, we can determine if [x−(3−2i)] is a factor of f(x).

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Find the area of the larger sector.
Round to the nearest tenth.
2559
13.4 miles
Area = [ ? ]miles2
Enter

Answers

Step-by-step explanation:

the formula for the area of a sector is

(x°(r^2)π)/360

with x being the angle

r bring the radius of the circle

(255(13.4)^2π)/360

399.6

Hope that helps :)

Answer:

The answer is 399.6 not 399.4. I put 399.6 as my answer on acellus and I got it right.

Which table represents a linear function?

Answers

Table one represents a linear function for the given data.

What is a linear function?

A linear function is a mathematical function that can be written in the form:

y = mx + b

where "m" and "b" are constants, and "x" and "y" are variables.

In this form, "m" represents the slope of the line, and "b" represents the y-intercept, the point where the line crosses the y-axis. The slope of the line is the rate of change of the function, representing how much the value of "y" changes for every unit change in "x".

The given table is,

x         y

1         5

2       10

3       15

4       20

5       25

The slope of the given data is,

m = ( 10 - 5 ) / ( 2 - 1 ) = 5

m = ( 15 - 10 ) / ( 3 - 2 ) = 5

m = ( 20 - 15 ) / ( 4 - 3 ) = 5

Here the slope is constant, so the function is linear.

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