Question

Scenario 7 Assume there is no seasonal affect on the birth of babies (humans). A member of a book club determines that of the 120 members, 35 were born in spring, 32 in summer, 28 in fall, and 25 in winter. This member wonders if in fact, human births are not uniform throughout the seasons. Questions 29 to 31 pertain to Scenario 7. Question 29 (1 point) Saved What is the expected number of births in each season - spring, summer, fall, winter - under the original assumption? Question 29 options: a) 35, 32, 28, 25 b) 30, 30, 30, 30 c) 32, 35, 25, 28 d) 32, 28, 28, 32 Question 30 (1 point) Saved What is (calculate) the chi-square statistic? Question 30 options: a) 1.833 b) 1.933 c) 2.033 d) 2.133 Question 31 (1 point) Saved How many degrees of freedom does the chi-square statistic have? Question 31 options: a) 2 b) 1 c) 4 d) 3

Answer 1

Solution:

Given:

Assume there is no seasonal affect on the birth of babies.

A member of a book club determines that of the 120 members,

35 were born in spring,

32 in summer,

28 in fall, and

25 in winter.

Question 29) What is the expected number of births in each season - spring, summer, fall, winter - under the original assumption?

If there is no seasonal affect on the birth of babies, then number of babies born in each season are same or equal.

We have N = 120 ,

Thus   the expected number of births in each season = 120 / 4 = 30

thus correct answer is: b) 30, 30, 30, 30

Question 30) What is (calculate) the chi-square statistic?

Chi square test statistic for goodness of fit

Where

O_i = Observed Counts

E_i =Expected Counts

Thus we need to make following table:

Season	Oi: Observed frequency	Ei: Expected Frequencies	Oi2/Ei
Spring	35	30	40.833
Summer	32	30	34.133
Fall	28	30	26.133
Winter	25	30	20.833
	N = 120

Thus

Thus correct answer is:  b) 1.933

Question 31) How many degrees of freedom does the chi-square statistic have?

Degrees of freedom = k - 1

where k = number of seasons = 4

thus

Degrees of freedom = k - 1

Degrees of freedom = 4 - 1

Degrees of freedom = 3

Thus correct answer is: d) 3