Mathematics, 02.04.2020 03:24 chaofails

Bara Research Group conducted a survey about church attendance. The survey respondents were asked about their church attendance and asked to indicate their age. Use the sample data to determine whether church attendance is independent of age. Using a level of significance, what is the p-value. Use alpha = 0.05.Church Attendance 20-29 30-39 40-49 50-59Yes 31 63 94 72No 69 87 106 78

Answers: 2

Show answers

Answers

Answer from: steven0448

The p-value is

- Select your answer -

between .025 and .05

between .05 and .025

between .015 and .045

What is your conclusion?

- Select your answer -

Conclude church attendance is not independent of age.

Conclude church attendance is independent of age.

What conclusion can you draw about church attendance, as individuals grow older?

- Select your answer -

Church attendance increases as individuals grow older.

Church attendance decreases the grow older.

Step-by-step explanation:

Hello!

There was a survey conducted where the people were asked two questions if they attended church and their age, both answers were recorded, so there are two variables of interest:

X₁: Church attendance, categorized: "Yes" and "No"

X₂: Age of the surveyed person, categorized: "20 to 29", "30 to 39", "40 to 49" and "50 to 59"

The objective is to test if both variables are independent so the hypothesis is:

H₀: Pij= Pi. * P.j ∀ i= 1, 2 and j= 1, 2, 3, 4

H₁: The categorized variables are not independent.

α: 0.05

Tho test this you have to conduct a Chi-Square test of independence, and the statistic is:

$X^2= sum(\frac{(O_{ij}-E_{ij})^2}{E_{ij}} )~~X^2_{(r-1)(c-1)}$

Before calculating the value of the statistic under the null hypothesis you have to calculate all expected frequencies using the following formula:

Eij= (Oi.*O.j)/n

E₁₁= (O₁.*O.₁)/n= (260*100)/600= 43.33

E₁₂= (O₁.*O.₂)/n= (260*150)/600= 65

E₁₃= (O₁.*O.₃)/n= (260*200)/600= 86.67

E₁₄= (O₁.*O.₄)/n= (260*150)/600= 65

E₂₁= (O₂.*O.₁)/n= (340*100)/600= 56.67

E₂₂= (O₂.*O.₂)/n= (340*150)/600= 85

E₂₃= (O₂.*O.₃)/n= (340*200)/600= 113.33

E₂₄= (O₂.*O.₄)/n= (340*150)/600= 85

$X^2= \frac{(31-43.33)^2}{43.33} +\frac{(63-65)^2}{65} +\frac{(94-86.67)^2}{86.67} +\frac{(72-65)^2}{65} +\frac{(69-56.67)^2}{56.67} +\frac{(87-85)^2}{85} +\frac{(106-113.33)^2}{113.33} +\frac{(78-85)^2}{85}$

$X^2_{H_0}= 8.72$

The rejection region for this test is one-tailed to the right with critical value:

$X^2_{(r-1)(c-1);1-\alpha }= X^2_{3;0.95}= 7.815$

The p-value for this test is also one-tailed and is

p-value: 0.033255

This p-value is less than the significance level, so the decision is to reject the null hypothesis. At a level of 5%, you can say that church attendance and the age of the people surveyed are not independent.

I hope it helps!

Bara Research Group conducted a survey about church attendance. The survey respondents were asked ab

Answer from: Quest

chicken chicken chicken

step-by-step explanation:

Answer from: Quest

Maybe fx = lxl because of the way the x is positioned is that what he

Another question on Mathematics

Mathematics, 21.06.2019 15:50

Assemble the proof by dragging tiles to the statements and reasons column

Answers: 2

Answer

Mathematics, 21.06.2019 17:00

Asap i need it now choose all the answers that apply. sex-linked disorders affect males more than females affect females more than males can be carried by females, without being expressed are always expressed in males are caused by genes carried on the x and y chromosomes

Answers: 1

Answer

Mathematics, 21.06.2019 19:20

Which number completes the system of linear inequalities represented by the graph? y> 2x – 2 and x + 4y 2 et 2 3 4

Answers: 3

Answer

Mathematics, 21.06.2019 19:50

Is it greater than or less than7*3_9*2

Answers: 2

Answer

You know the right answer?

Bara Research Group conducted a survey about church attendance. The survey respondents were asked ab...