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
umka2103 [35]
3 years ago
14

If there is no seasonal effect on human births, we would expect equal numbers of children to be born in each season (winter, spr

ing, summer, and fall). A student takes a census of her statistics class and finds that of the 120 students in the class, 25 were born in winter, 35 in spring, 32 in summer, and 28 in fall. She wonders if the excess in the spring is an indication that births are not uniform throughout the year. a) What is the expected number of births in each season if there is no "seasonal effect" on births? b) Compute the x2 statistic. c) How many degrees of freedom does the x2 statistic have? d) Find the a = 0.05 critical value for the x2 distribution with the appropriate number of df. e) Using the critical value, what do you conclude about the null hypothesis at a = 0.05?
Mathematics
1 answer:
Minchanka [31]3 years ago
5 0

Answer:

Step-by-step explanation:

Hello!

Given the variable of interest:

X: Number of births in each season of the year, categorized: W: Winter, Sp: Spring, Su: Summer and F: Fall

The objective is to test if there is no seasonal effect on human births. If this is true, then you would expect the proportion of births to be the same through all seasons. This means that, theoretically, you could expect that P(W)=P(Sp)=P(Su)=P(F)=1/4

To test this out a student made a census in her class and obtained the following observations:

n= 120 students surveyed

25 were born in Winter

35 were born in Spring

32 were born in Summer

28 were born in Fall

The appropriate statistic analysis to test the student's presumption is a Goodness to Fit Chi-Square test, with hypotheses:

H_{0}: P_{W}=P_{Sp}=P_{Su}=P_{F}=1/4

H₁: At least one of the proportions is different from the others.

a) To calculate the expected frequency for each category you have to use the following formula Ei= n*Pi

Where Pi represents the expected proportion for the i-category.

In this particular case, the expected proportion for all categories is the same so the expected frequency will also be the same:

E_{W}= n*P_{W}= 120*1/4= 30\\E_{Sp}= n*P_{Sp}= 120*1/4=30\\E_{Su}= n*P_{Su}= 120*1/4=30\\E_{F}= n*P_{F}= 120*1/4=30

b)

X²=∑\frac{(Oi-Ei)^2}{Ei}~X^2_{k-1}

X^2_{H_0}= \frac{(25-30)^2}{30} + \frac{(35-30)^2}{30} + \frac{(32-30)^2}{30} + \frac{(28-30)^2}{30} = 1.93

c)

The statistic for this test has k-1 degrees of freedom, where k represents the number of categories of the variable. In this case, the statistic has 4-1=3 degrees of freedom.

d)

The rejection region for the Goodnes to Fit test is <u>always</u> one-tailed to the right, wich means that you'll reject the null hypothesis to big values of X²:

X^2_{k-1;1-\alpha }= X^2_{3;0.95}= 7.815

The decision rule is:

If X^2_{H_0} ≥ 7.815, reject the null hypothesis

If X^2_{H_0} < 7.815, do not reject the null hypothesis

e)

X^2_{H_0}= 1.93 is less than the critical value 7.815, so the decision is to not reject the null hypothesis.

Using a 5% level of significance, there is no significant evidence to reject the null hypothesis. Then you can conclude that there is no seasonal effect on human birth, i.e. the expected birth proportions are the same through all seasons.

I hope this helps!

You might be interested in
Solve for f.<br><br> 8 = 2f + 2
tiny-mole [99]

Answer:

f = 3

Step-by-step explanation:

8 = 2f + 2

-2         -2

6 = 2f

/2    /2

3 = f

5 0
3 years ago
a shoreline is changing -3 centimeters each year due to erosion. what is the change in shoreline over 6 years?
NikAS [45]

Answer:

-18

Step-by-step explanation:

3 0
3 years ago
1
ipn [44]

Answer:

my fault pimp i aint know the answer

Step-by-step explanation:

my fault pimp i aint know the answer

my fault pimp i aint know the answer

my fault pimp i aint know the answer

my fault pimp i aint know the answer

my fault pimp i aint know the answer

4 0
3 years ago
The library made a table to track the number of fiction and nonfiction books checked out for 6 days.
coldgirl [10]

Answer:

18 fiction = 3

12 non fiction= 2

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What is the distributive property? ​
Bumek [7]

Answer:

2(x + y) = 2x + 2y

Hope this helped and brainliest please

8 0
2 years ago
Read 2 more answers
Other questions:
  • Jillian is making curtains for her room. She has fabric for each curtain that is 1.6 meters in length. She folds the bottom of t
    11·1 answer
  • james has a board that is 3/4 long he wants to cut the board into 1/8 pieces how many pieces can james cut from the board write
    12·1 answer
  • Calculate the perimeter of each figure <br> How do you find the perimeter of a figure
    12·1 answer
  • Which expression is equivalent to 3x+10-x+12
    12·1 answer
  • Don is buying a home for $190,300.He is making a 30% down payment and financing the rest with a 15 – year loan at 5.75% interest
    12·2 answers
  • What would the answer be because I already tried everything and I just can’t get it
    6·2 answers
  • Which measure is most appropriate to describe the center of the data in the stem-and-leaf plot below?
    6·2 answers
  • Math Help!!
    6·1 answer
  • Solve each of the following equations show solution set on a number line 3x-1=8
    7·1 answer
  • What is 3 as a fraction? An the 3 isn't in percentage.... its just three.
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!