Expression with the same value

A researcher classifies firefighters according to whether their gloves fit well or poorly and by gender. They want to know if th

snow_tiger [21]

Answer:

Step-by-step explanation:

Hello!

The objective is to test if the proportion of "X: gloves fitness, categorized: Fit poorly and Fit well" is the same for two populations of interest, "male firefighters" and "female firefighters"

To do this you have to conduct a Chi-Square test of Homogeneity.

In the null hypothesis you have to state that the proportion of the categories of the variable are the same for all the populations of interest.

Be

M: the firefighter is male

F: the firefighter is female

Y: represents the category that the gloves "fit poorly"

W: represents the category that the gloves "fit well"

The null hypothesis will be:

H₀: P(Y|M)=P(Y|F)=P(Y)

P(W|M)=P(W|F)=P(W)

H₁: At least one of the statements in the null hypothesis is false.

α: 0.01

To calculate the statistic under the null hypothesis you have to calculate the expected frequencies first:

$E_{ij}= O_{.j}*\frac{O_{i.}}{n}$

O.j= total of the j-column

Oi.= total of the i-row

n= total of observations

$E_{11}= 547*\frac{152}{586} = 141.88$

$E_{12}=39*\frac{152}{586}= 10.12$

$E_{21}= 547*\frac{434}{586} = 405.12$

$E_{22}= 39*\frac{434}{586} = 28.88$

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

r= number of rows (in this case 2)

c=number of columns (in this case 2)

$X^2_{H_0}= \frac{(132-141.88)^2}{141.88} +\frac{(20-10.12)^2}{10.12} +\frac{(415-405.12)^2}{405.12} +\frac{(19-28.88)^2}{28.88} = 13.95$

Using the critical value approach, you have to remember that this test is <em><u>always</u></em> one-tailed to the right, meaning that you'll have only one critical value from which the rejection region is defined:

$X^2_{(r-1)(c-1);1-\alpha }= X^2_{1;0.99}= 6.635$

The decision rule is then:

If $X^2_{H_0}$ ≥ 6.635, reject the null hypothesis.

If $X^2_{H_0}$ < 6.635, do not reject the null hypothesis.

The calculated value is greater than the critical value, the decision is to reject the null hypothesis.

So at a 1% level you can conclude that this test is significant. This means that the proportions of gloves fitness, categorized in "Fit poorly" and "Fit well" are different for the male and female firefighters populations.

I hope this helps!

3 0

3 years ago

Read 2 more answers

James would like to learn how to make omelettes. He polls his family about the number of eggs they each use to make one. He gets

Dmitry_Shevchenko [17]

Answer:

2 eggs

Step-by-step explanation:

Mean is average, so add all the numbers together then divide by how many numbers there are.

3 + 3 + 2+ 3 + 1 + 2 + 1 + 1 = 16

16 ÷ 8 = 2

4 0

2 years ago

A man gathers nuts in a forest. Each time he finds a nut, there is a 20% chance it is a pecan and a 35% chance it is a walnut.

gladu [14]

Either a pecan or walnut means you add the probabilities together

20% plus 35% equals 55%

7 0

3 years ago

After 45 seconds, Camden’s bathtub fills with 3 inches of water. How many seconds will it take to fill Camden’s tub with 20 inch

Pepsi [2]

So you have to find how many seconds it takes to fill up with 1 inch.
TO find that, you have to divide 45/3 which equals to 15.
So it takes 15 seconds for 1 inch. The question is asking you to find out how many seconds will it take to fill the tub with 20 inches.
SO your gonna multiply 15*20.
15*20 = 300
So it would take 300 seconds to fill up Camden's tub.

5 0

3 years ago

You make a scale drawing of a tree using the scale 5 in. =27 ft. If the tree is 67.5 ft tall, how tall is the scale drawing?

wel

5in. 27ft
X in. 67.5ft
X=5•67.5/27
X=12.5 in

8 0

3 years ago