1. A civil rights group feels that the selection of
contestants on a game show program is biased against blacks. The
U.S. Census Bureau reports that 12.7% of all U.S. citizens are
black. Suppose we can assume that the contestants who have
already appeared may be treated as essentially a random sample
drawn from all contestants who may ever appear. Of these
appearing contestants there have been 212 whites (nonHispanic),
13 blacks, 17 Hispanics, and 3 Asians. Test the groups claim:
state hypotheses, compute the test statistic and obtain the *P*-value.
Interpret the *P*-value. Is there sufficient evidence to
conclude that the civil rights group is correct? Use a 1%
significance level to make a decision. In practical terms, what
issues must be considered before accusing the game show of
discrimination?

2. According to the U.S. Census Bureau's most recent reported statistics (1998), what percentage of U.S. citizens fall into each of the following groups? (I've already given you one figure above.)

White non Hispanic | ______ % |

Black | ______ % |

Asian & Pacific Islander | ______ % |

American Indian, Eskimo, Aleut | ______ % |

Hispanic | ______ % |

What percentage are female?

3. In a *Pepsi* ad, the claim is made that "in
recent blind taste tests, more than half the *Coke*
drinkers said they preferred the taste of *Pepsi*."
In this test, 100 *Coke* drinkers took the "*Pepsi*
Challenge" and 57 prefered the taste of *Pepsi*. Use
this data to test the alternative hypothesis that more than half
of ALL *Coke* drinkers will prefer *Pepsi* in a
blind taste test: state hypotheses, compute the test statistic
and obtain the *P*-value. Interpret the *P*-value.
If testing at the 5% level, what do you conclude? Suppose 65
preferred *Pepsi*. Without computing: Would the *P*-value
be larger, smaller, or the same as what you've just obtained? Now,
compute it and see if you're right.

1. We're testing H_{0}: *p* = .127 H_{A}:
*p* < .127 where *p* is the proportion of
all game show contestants who are black. The test statistic is *Z
*= -3.48 and the *P*-value is .0003. When the null
hypothesis is true there is a 1 in 3333 (=.0003) chance of
observing data such as ours (only 13 of 245, or 5.31% black).
Inference: the null hypothesis probably is not true. At that 1%
significance level we reject the null and conclude that the
blacks have less that 12.7% chance of participating on the show.

2. Find out for yourself! It's on the net. Try the U.S. Census Bureau.

3. We're testing H_{0}: *p* = .5 H_{A}:
*p* > .5 where *p* is the proportion of
all *Coke* drinkers who prefer *Pepsi* when tested.
The test statistic is *Z *= 1.40 and the *P*-value
is .0808. When the null hypothesis is true there is about a 1 in
12 chance of observing data such as ours (the 57%). Inference:
there's some evidence that the null hypothesis is not true -- but
it's hardly compelling. At that 5% significance level we are
unable to reject the null hypothesis. If 65 out of 100 had
preferred *Pepsi* we'd have * more*
evidence against the null hypothesis -- consequentlly the