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
navik [9.2K]
3 years ago
12

Is education related to programming preference when watching TV? From a poll of 80 television viewers, the following data have b

een collected: Level of Education Preferred TV stations High School Some college Bachelor’s degree or higher Total Public Broadcasting 15 15 10 40 Commercial Stations 5 25 10 40 Total 20 40 20 80 Test the null hypothesis that there is no association between level of education and TV station preference. A. State the null and alternative hypotheses. B. Calculate a test statistic, C. At the .05 level of significance, state the critical value, D. State your decision and conclusion.
Mathematics
1 answer:
Luda [366]3 years ago
7 0

Answer:

a) H0:  There is no association between level of education and TV station preference (Independence)

H1: There is association between level of education and TV station preference (No independence)

b) \chi^2 = \frac{(15-10)^2}{10}+\frac{(15-20)^2}{20}+\frac{(10-10)^2}{10}+\frac{(5-10)^2}{10}+\frac{(25-10)^2}{10}+\frac{(10-20)^2}{20} =33.75

c) \chi^2_{crit}=5.991

d) Since the p value is lower than the significance level we enough evidence to reject the null hypothesis at 5% of significance, and we can conclude that we have dependence between the two variables analyzed.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

                                  High school   Some College   Bachelor or higher  Total

Public Broadcasting       15                       15                          10                     40

Commercial stations      5                         25                         10                     40  

Total                                20                      40                          20                    80

We need to conduct a chi square test in order to check the following hypothesis:

Part a

H0:  There is no association between level of education and TV station preference (Independence)

H1: There is association between level of education and TV station preference (No independence)

The level os significance assumed for this case is \alpha=0.05

The statistic to check the hypothesis is given by:

\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}

Part b

The table given represent the observed values, we just need to calculate the expected values with the following formula E_i = \frac{total col * total row}{grand total}

And the calculations are given by:

E_{1} =\frac{20*40}{80}=10

E_{2} =\frac{40*40}{80}=20

E_{3} =\frac{20*40}{80}=10

E_{4} =\frac{20*40}{80}=10

E_{5} =\frac{40*40}{80}=20

E_{6} =\frac{20*40}{80}=10

And the expected values are given by:

                                  High school   Some College   Bachelor or higher  Total

Public Broadcasting       10                       20                         10                     40

Commercial stations      10                        10                         20                     40  

Total                                20                      30                          30                    80

Part b

And now we can calculate the statistic:

\chi^2 = \frac{(15-10)^2}{10}+\frac{(15-20)^2}{20}+\frac{(10-10)^2}{10}+\frac{(5-10)^2}{10}+\frac{(25-10)^2}{10}+\frac{(10-20)^2}{20} =33.75

Now we can calculate the degrees of freedom for the statistic given by:

df=(rows-1)(cols-1)=(2-1)(3-1)=2

Part c

In order to find the critical value we need to look on the right tail of the chi square distribution with 2 degrees of freedom a value that accumulates 0.05 of the area. And this value is \chi^2_{crit}=5.991

Part d

And we can calculate the p value given by:

p_v = P(\chi^2_{3} >33.75)=2.23x10^{-7}

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(33.75,2,TRUE)"

Since the p value is lower than the significance level we enough evidence to reject the null hypothesis at 5% of significance, and we can conclude that we have dependence between the two variables analyzed.

You might be interested in
What is the missing number in this pattern?<br> 0, 2, 6, ----, 30, 62
mario62 [17]

Answer:

14

Step-by-step explanation:

so the pattern is they add 2 then they add 4 then they add 8 then the add 16 basically they are double the number being added each number so the missing number is 14

5 0
2 years ago
Read 2 more answers
Joshua has a ladder that is 25 ft long....HELP!!
madreJ [45]
For example 1ft = 12in so 12 is the number that you are going to multiply so just multiply 25×12 and that is your answer
7 0
3 years ago
Read 2 more answers
20 Points! <br><br> Solve for x
Marrrta [24]

Answer:

so all x's have to be added together.

8x+5x+10x+7x=30x

-2+3=1

1dividedby30=30

x=30

hope this helps


7 0
3 years ago
Read 2 more answers
Which table shows exponential decay?
alexandr402 [8]

Answer:

Table 1,

1 16

2 8

3 4

4 2

Step-by-step explanation

The equation for this function can be written as

y = 16^1/x

This is exponential decay.  

7 0
3 years ago
Read 2 more answers
Simplify the expression:<br> 4n + 7 +6
Elan Coil [88]

Answer:

4n+13

Step-by-step explanation:

combine like terms.

8 0
3 years ago
Read 2 more answers
Other questions:
  • » A cylinder has a height of 13 millimeters and a radius of 11 millimeters. What is its
    15·2 answers
  • The diameter of a cylindrical construction pipe is 4 ft. If the pipe is 16 ft long, what is its volume?
    13·2 answers
  • How do you figure out 3/2 divide 1/4=N. What is n between
    14·1 answer
  • A cake recipe calls for 30 milliliters of water for every 20 milliliters of cooking oil. How many milliliters of water are neede
    12·1 answer
  • 3. Of the 32 students in Maria's class, 14 play sports, 19 are in the band, and 6 are involved in both sports and
    7·1 answer
  • I NEED HELP ASAP!<br><br> You pick a card at random.<br><br> 2345<br><br> What is P(odd or prime)?
    8·2 answers
  • A-32=47 what the equation for a
    8·2 answers
  • Please solve, might be last question of the day for me.
    7·1 answer
  • At hms 60% of the students voted in an election if there are 1,500 students how many voted
    11·2 answers
  • I need help on the last one
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!