Employment discrimination? Census data for New York City indicate that $29.2 \%$ of the under-18 population is white, $28.2 \%$ black, $31.5 \%$ Latino, $9.1 \%$ Asian, and $2 \%$ are of other ethnicities. The New York Civil Liberties Union points out that of 26,181 police officers, $64.8 \%$ are white, $14.5 \%$ are black, $19.1\%$ Hispanic, and $1.4\%$ Asian. Do the police officers reflect the ethnic composition of the city's youth? (Equate Latino with Hispanic.)

b) Review the assumptions.

After getting trounced by your little brother in a children's game, you doubt that the death he gave you is unfair. To review, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on the die's fairness?

e) How many degrees of freedom are there?

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) What is the expected number of births in each season if there is no "seasonal effect" on births? b) Compute the

$$X^2$$

statistic. c) How many degrees of freedom does the

$$X^2$$

statistic have?

After getting trounced by your little brother in a children's game, you suspect the die he gave you to roll may be unfair. To check, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on the die's fairness?

$$\begin{aligned} &\begin{array}{r|r} \text { Face}&\text{ Count }\\ 1 & 11 \\ 2 & 7 \\ 3 & 9 \\ 4 & 15 \\ 5 & 12 \\ 6 & 6 \end{array} \end{aligned}$$

Find $\chi^2$ and the P-value and State your conclusion.

After getting trounced by your little brother in a children's game, you doubt that the death he gave you is unfair. To review, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on the die's fairness?

b) To see if these results are unusual, will you test goodness-of-fit, homogeneity, or independence?

After getting trounced by your little brother in a children's game, you doubt that the death he gave you is unfair. To review, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on the die's fairness?

c) State your hypotheses.

After getting trounced by your little brother in a children's game, you doubt that the death he gave you is unfair. To review, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on the die's fairness?

g) State your conclusion.

After getting trounced by your little brother in a children's game, you doubt that the death he gave you is unfair. To review, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on the die's fairness?

d) Check the conditions.

After getting trounced by your little brother in a children's game, you suspect the die he gave you to roll may be unfair. To check, you plan to roll it 60 times, recording the number of times each face appears. a) What's your null hypothesis? b) Write the alternative hypothesis.

The table in the earlier exercise shows whether NEJM medical articles during various time periods included statistics or not. We're planning to do a chi-square test.

The smallest expected count will be in the 1989/No cell. What is it?

We've begun to examine whether the use of statistics in NEJM medical articles has changed over time.

a) Calculate the component of chi-square for the 1989/ No cell.

b) For this test, $\chi^2=25.28$. What's the P-value?

c) State your conclusion.

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. What is the expected number of births in each season if there is no "seasonal effect" on births?

In the earlier exercises, we've begun to examine whether the use of statistics in NEJM medical articles has changed over time.

Calculate the component of chi-square for the 1989/No cell.

In the earlier exercises, we've begun to examine whether the use of statistics in NEJM medical articles has changed over time.

For this test, $\chi^2$ = 25.28. What's the P-value?