1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Amiraneli [1.4K]
3 years ago
7

A researcher used a sample of n = 60 individuals to determine whether there are any preferences among six brands of pizza. Each

individual tastes all six brands and selects his/her favorite. If the data are evaluated with a chi-square test for goodness of fit using α = .05, then how large does the chi-square statistic need to be to reject the null hypothesis?
7. A chi-square test for goodness of fit is used to examine the distribution of individuals across four categories, and a chi-square test for independence is used to examine the distribution of individuals in a 2×2 matrix of categories. Which test has the larger value for df?

8. A sample of 100 people is classified by gender (male/female) and by whether or not they are registered voters. The sample consists of 80 females and 20 males, and has a total of 60 registered voters. If these data are used for a chi-square test for independence, what is the total number of females for the expected frequencies?

9. What is stated by the null hypothesis for the chi-square test for independence?

10. A chi-square test for independence is being used to evaluate the relationship between two variables, one of which is classified into 3 categories and the second of which is classified into 4 categories. The chi-square statistic for this test would have df equal to ______.
Mathematics
1 answer:
Blizzard [7]3 years ago
4 0

Answer:

1) χ² ≥ 11.07

2) Goodness of fit test, df: χ²_{3}

Independence test, df: χ²_{1}

The goodness of fit test has more degrees of freedom than the independence test.

3) e_{females.} = 80

4) H₀: P_{ij}= P_{i.} * P_{.j} ∀ i= 1, 2, ..., r and j= 1, 2, ..., c

5) χ²_{6}

Step-by-step explanation:

Hello!

1)

The researcher took a sample of n=60 people and made them taste proof samples of six different brands of pizza and choose their favorite brand, their choose was recorded. So the study variable is the following:

X: favorite pizza brand, categorized in brand 1, brand 2, brand 3, brand 4, brand 5 and brand 6.

The Chi-square goodness of fit test is done with the following statistic:

χ²= ∑\frac{(O_i-E_i)^2}{E_i} ≈χ²_{k-1}

Where k represents the number of categories of the study variable. In this example k= 6.

Remember, the rejection region for the Chi-square tests of "goodnedd of fit", "independence", and "homogeneity" is allways one-tailed to the right. So you will only have one critical value.

χ²_{k-1; 1 - \alpha }

χ²_{6-1; 1 - 0.05 }

χ²_{5; 0.95 } = 11.070

This means thar the rejection region is χ² ≥ 11.07

If the Chi-Square statistic is equal or greather than 11.07, then you reject the null hypothesis.

2)

The statistic for the goodness of fit is:

χ²= ∑\frac{(O_i-E_i)^2}{E_i} ≈χ²_{k-1}

Degrees of freedom: χ²_{k-1}

In the example: k= 4 (the variable has 4 categories)

χ²_{4-1} = χ²_{3}

The statistic for the independence test is:

χ²= ∑∑\frac{(O_ij-E_ij)^2}{E_ij} ≈χ²_{(r-1)(c-1)} ∀ i= 1, 2, ..., r & j= 1, 2, ..., c

If the information is in a contingency table

r= represents the total of rows

c= represents the total of columns

In the example: c= 2 and r= 2

Degrees of freedom: χ²_{(r-1)(c-1)}

χ²_{(2-1)(2-1)} = χ²_{1}

The goodness of fit test has more degrees of freedom than the independence test.

3)

To calculate the expected frecuencies for the independence test you have to use the following formula.

e_{ij} = n * P_i. * P_.j = n * \frac{o_i.}{n} * \frac{o_.j}{n}

Where o_i. represents the total observations of the i-row, o_.j represents the total of observations of the j-column and n is the sample size.

Now, this is for the expected frequencies in the body of the contingency table, this means the observed and expected frequencies for each crossing of categories is not the same.

On the other hand, you would have the totals of each category and population in the margins of the table (subtotals), this is the same when looking at the observed frequencies and the expected frequencies. Wich means that the expected frequency for the total of a population is the same as the observed frequency of said population. A quick method to check if your calculations of the expected frequencies for one category/population are correct is to add them, if the sum results in the subtotal of that category/population, it means that you have calculated the expected frequencies correctly.

The expected frequency for the total of females is 80

Using the formula:

(If the females are in a row) e_{females.} = 100 * \frac{80}{100} * \frac{0}{100}

e_{females.} = 80

4)

There are two ways of writing down a null hypothesis for the independence test:

Way 1: using colloquial language

H₀: The variables X and Y are independent

Way 2: Symbolically

H₀: P_{ij}= P_{i.} * P_{.j} ∀ i= 1, 2, ..., r and j= 1, 2, ..., c

This type of hypothesis follows from the definition of independent events, where if we have events A and B independent of each other, the probability of A and B is equal to the product of the probability of A and the probability of B, symbolically: P(A∩B) = P(A) * P(B)

5)

In this example, you have an independence test for two variables.

Variable 1, has 3 categories

Variable 2, has 4 categories

To follow the notation, let's say that variable 1 is in the rows and variable 2 is in the columns of the contingency table.

The statistic for this test is:

χ²= ∑∑\frac{(O_ij-E_ij)^2}{E_ij} ≈χ²_{(r-1)(c-1)} ∀ i= 1, 2, ..., r & j= 1, 2, ..., c

In the example: c= 3 and r= 4

Degrees of freedom: χ²_{(r-1)(c-1)}

χ²_{(3-1)(4-1)} = χ²_{6}

I hope you have a SUPER day!

You might be interested in
If the variance of the "number of daily parking tickets issued is 100, the standard deviation is defined as the _____________. A
Alex17521 [72]

Answer:

Square root of the variance of the "number of daily parking tickets"

Step-by-step explanation:

The Standard Deviation is a measure of how spread out numbers are.

Its symbol is σ (the Greek letter sigma)

The formula is easy: it is the square root of the Variance.

8 0
3 years ago
The sum of 3 numbers is -44.84.one of these numbers is 24.6.the other 2 numbers are equal to each number.what is the value of ea
Bad White [126]
X+24.6=-44.84
Subtract 24.6 /2

X= -34.72
5 0
3 years ago
A hot-air balloon at 1020 feet descends at a rate of 85 feet per minute. Let y represent the height of the balloon and let x rep
Lady_Fox [76]
Y=1020-85x because since it's a decrease it would be goung do, hence the subtraction
8 0
3 years ago
Omarie picked x amount of apples, took a break, and then picked v more. Write the expression that models the total number of app
meriva

Answer:

x+v

Step-by-step explanation:

i hope this halps =3

brainliest?

5 0
2 years ago
Solve the following system of equations.
Yuri [45]

Answer:

x= 12

y= 10

best of luck mate

7 0
2 years ago
Other questions:
  • What's the correct answer? Thank you!
    5·2 answers
  • The step work of the question along with the answer​
    10·1 answer
  • 15/25 in lowest terms
    10·2 answers
  • What is the difference between 36.92 and 4.218?
    14·2 answers
  • Bradley is returning home from a place that is 2 kilometers away. The function y = 2,000 − 90x represents Bradley's distance fro
    14·1 answer
  • Solve formula for specified variable V=AMJ for A
    15·1 answer
  • Denise is constructing a square. she has already used her straightedge and compass to construct the circle, lines, and arcs show
    13·1 answer
  • Will give you brainlyist pls help​
    13·1 answer
  • Help please I need the answer
    7·2 answers
  • ¿Cuál es la expresión algebraica que representa el área del rectángulo?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!