Question

If there is no seasonal effect on human​ births, we would expect equal numbers of children to be born in each season​ (winter, spring,​ 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, 36 in​ spring, 33 in​ summer, and 26 in fall. She wonders if the excess in the spring is an indication that births are not uniform throughout the year. Complete parts a through c below.

​a) Compute the standardized residual for each season.

	Standardized Residual
Winter	nothing
Spring	nothing
Summer	nothing
Fall	nothing
	​(Round to three decimal places as​ needed.)

​b) Are any of the standardized residuals particularly​ large? (Compared to​ what?)

A.

The standardized residuals are not particularly large compared to the value of the​ chi-square test statistic.

B.

The standardized residuals are particularly large compared to the value of the​ chi-square test statistic.

C.

The standardized residuals are​ z-scores and at least one of them is particularly​ large, having a magnitude greater than 2.

D.The standardized residuals are​ z-scores and not particularly large because they are between

negative 2−2

and 2.

​c) Determine the null and alternative hypotheses. Choose the correct answer below.

A.

Upper H 0H0​:

Births are not distributed uniformly across the seasons.

Upper H Subscript Upper AHA​:

Births are distributed uniformly across the seasons.

B.

Upper H 0H0​:

Births are distributed uniformly across the seasons.

Upper H Subscript Upper AHA​:

Births are not distributed uniformly across the seasons.

C.

Upper H 0H0​:

Births are distributed uniformly across the seasons.

Upper H Subscript Upper AHA​:

All the probabilities are different.

D.

Upper H 0H0​:

All the probabilities are different.

Upper H Subscript Upper AHA​:

Births are distributed uniformly across the seasons.

Find the alphaαequals=0.05 critical value for the chi squaredχ2 distribution with 3 degrees of freedom.

chi squaredχ2=___

​(Round to two decimal places as​ needed.)

Why should you have anticipated the answer to part​ b? (The computed

chi squaredχ2 statistic for the given data is 2.87​.)

Since the test statistic is (less than greater than) the critical​ value, (fail to reject, reject) H0. Because of this​ conclusion, ___at least one none all of the standardized residuals should be expected to be large in magnitude.

Answer 1