1 answer

A researcher wanted to determine if babies were born at different rates in different months. Tracking...

Question:

A researcher wanted to determine if babies were born at different rates in different months. Tracking a random sample of birth records for one metropolitan area resulted in the following data. Use a chi-square critical value of 19.675.

Jan

Feb

Mar

Apr

May

June

July

Aug

Sept

Oct

Nov

Dec

Observed

14

12

12

10

16

9

16

11

21

8

24

9

  1. What are the null and alternate hypothesis for this test?
  2. What is the expected number of babies for each month? Report as a decimal, if applicable.
  3. Calculate the chi-square statistic. Show your work for at least one cell calculation and the final statistic.
  4. Write a complete conclusion citing your statistics.

Answers

a)

Null hypothesis: Babies are born uniformly in all 12 months

ALternate hypothesis Ha: Babies are not born uniformly in all 12 months

b)

expected value =np=162*(1/12) =13.5

c)

applying chi square goodness of fit test:
           relative observed Expected residual Chi square
category frequency(p) Oi Ei=total*p R2i=(Oi-Ei)/√Ei R2i=(Oi-Ei)2/Ei
Jan    1/12 14.000 13.500 0.14 0.019
Feb    1/12 12.000 13.500 -0.41 0.167
Mar    1/12 12.000 13.500 -0.41 0.167
Apr    1/12 10.000 13.500 -0.95 0.907
May    1/12 16.000 13.500 0.68 0.463
Jun    1/12 9.000 13.500 -1.22 1.500
Jul    1/12 16.000 13.500 0.68 0.463
Aug    1/12 11.000 13.500 -0.68 0.463
Sep    1/12 21.000 13.500 2.04 4.167
Oct    1/12 8.000 13.500 -1.50 2.241
Nov    1/12 24.000 13.500 2.86 8.167
Dec    1/12 9.000 13.500 -1.22 1.500
total 1.000 162 162 20.222
test statistic X2 = 20.222

d)

as test statistic is higher than critical value we reject null and conclude that  babies were born at different rates in different months.

.

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