Advanced High-School Mathematics

SECTION 6.6 χ^2 and Goodness of Fit 415

box can be modeled by a binomial distribution. He examines 100

boxes an obtains the following data:

Number of brown eggs in a box Frequency

0 10

1 29

2 31

3 18

4 8

5 3

6 1

(a) Estimate the percentagepof brown eggs in the population of

all eggs.

(b) How well does the binomial distribution with parameter p

model the above data? Test at the 5% level.

3. Suppose you take six coins and toss them simultaneously 100, lead-
   ing to the data below:

Number of heads

obtained

Frequency Expected underH 0

0 0

1 4

2 13

3 34

4 30

5 15

6 4

Suppose that I tell you that of these six coins, five are fair and

one has two heads. Test this as a null hypothesis at the 5% level.

(Start by filling in the expected counts under the appropriate null

hypothesis.)

4. Here’s a more extended exercise. In Exercise 18 on page 344 it
   was suggested that the histogram representing the number of trials