For the births in Exercise 1,
In exercise 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, 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) If there is no seasonal effect, about how big, on average, would you expect the x2 statistic to be (what is the mean of the x2 distribution)?
b) Does the statistic you computed in Exercise 1 seem large in comparison to this mean? Explain briefly.
c) What does that say about the null hypothesis?
d) Find the α = 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 α = 0.05?