Answer Happy

Are birthdays "evenly distributed" throughout the year, or are
they more common during some parts of the year than others? Owners
of a children's toy store chain in the Northwest asked just this
question. Some data collected by the chain are summarized in the
table below.
The data were obtained from a random sample of
200
people. The birthdate of each person was recorded, and
each of these dates was placed into one of four categories: winter
(December 21-March 20), spring (March 21-June 20), summer (June
21-September 20), and fall (September 21-December 20). The numbers
in the first row of the table are the frequencies observed in the
sample for these season categories. The numbers in the second row
are the expected frequencies under the assumption that birthdays
are equally likely during each season of the year. The bottom row
of numbers gives the following value for each of the season
categories.
−fOfE2
fE
=
−Observed frequencyExpected frequency2
Expected frequency
Part 1
Fill in the missing values in the table. Round your responses
for the expected frequencies to two or more decimal places. Round
your
−fOfE2fE
responses to three or more decimal places.
Send data to Excel
Winter
Spring
Summer
Fall
Total
Observed frequency
fO
fO
38
fO
39
fO
60
fO
63
200
Expected frequency
fE
fE
fE
fE
50.00
fE
50.00
−fOfE2fE
−fOfE2fE
−fOfE2fE
−fOfE2fE
2.000
−fOfE2fE
3.380
Part 2
Answer the following to summarize the test of the hypothesis
that birthdays are equally likely during each season of the year.
Use the
0.10
level of significance for the test.
(a) Determine the type of test statistic to use.
Type of test statistic: ▼(Choose one)
(b) Find the value of the test statistic. (Round your
answer to two or more decimal places.)
(c) Find the critical value. (Round your answer to two or
more decimal places.)
(d)Can we reject the hypothesis that birthdays are equally
likely during each season of the year?
Yes
No