Statistics 1060 : Practice Solutions Week 4

2.87

a) The overall percent of non response is total number of companies that did not respond divided by the total number of companies that received a questionnaire.

\begin{displaymath}\frac{nonresponce}{total} = \frac{75 + 119 + 160}{200 + 200 + 200} = \frac{354}{600} = 0.59\end{displaymath}

$59\%$ of the companies did not respond.

b) As before we can calculate what percent of each of the small, medium and large companies responded to the questionnaire. $37.5\%$ of the small companies, $59.5\%$ of medium-sized companies and $80\%$ of large companies did not respond. The relation between company and response is: Generally, the larger the company, the less likely it is to respond.

d) In total we have 125 + 81 + 40 = 246 responses. Of these responses $\frac{125}{246} = 0.508 = 50.8\%$ came from small companies, $32.9\%$ came from medium-sized companies and $16.3\%$ came from large companies.

e) Definitely not. More than half of the responses came from small businesses. The data would not give proper conclusions.

2.98

$58.3\%$ of desipramine did not relapse into drug use. There was a $25\%$ relapse for those treated with lithium and a $16.7\%$ relapse for those who were given placebos. Desipramine appears to be an effective drug in treating cocaine addiction.

2.91

a) The sum of the entries in the married column is 58,929 while the ``total" entry is 58,931. This is due to the round-off error. Each age group is rounded to the nearest thousand, while the total is obtained directly from the source before tabulation.

b) To obtain the marginal distribution of marital status for all adult woman we must divide each column total by the total number of woman. We get

$\begin{array}{lcccc}
Never \ Married & = & \frac{19312}{99588} = 0.194 & = & 19...
... 59.2\% \\
Widowed & & & = & 11.1\% \\
Divorced & & & = & 10.3\%
\end{array}$

c) We obtain this by dividing the number of 18 - 24 year olds in each division by the total in that division.

18 - 24 years

$\begin{array}{lcccc}
Never \ Married & = & \frac{9289}{12613} = 0.736 & = & 73....
... & 21.4\% \\
Widowed & & & = & 0.2\% \\
Divorced & & & = & 2.1\%
\end{array}$

40 - 64 years

$\begin{array}{lcc}
Never \ Married & = & 6.3\% \\
Married & = & 72.2\% \\
Widowed & = & 6.0\% \\
Divorced & = & 15.0\%
\end{array}$

Almost $75\%$ of the younger women have not been married. The younger woman that are married have not had time to become divorced or widowed. The majority of older woman are, or have been, married. Only about $6\%$ have not married.

d) The conditional distribution of age among single women (never married) is as follows:
$\begin{array}{lc}
18 - 24 & 48.1\% \\
25 - 39 & 36.0\% \\
40 - 64 & 11.9\% \\
65+ & 4.0\%
\end{array}$
The target area for this magazine would be under 39 years of age as this is what age most unmarried woman are.

2.93

a) Males: 490 admitted, 210 refused

Females: 280 admitted, 220 refused

b) $70\%$ of male applicants are admitted, $56\%$ of females are admitted.

c) In business, $80\%$ of male applicants are admitted and $90\%$ of female applicants are admitted. In law, $10\%$ of males are admitted and $33.3\%$ of females are admitted.

d) A majority of the male applicants apply to business school which admits $83\%$ of all applicants. A majority of women apply to law school, which only admits $27.5\%$ of its applicants.

2.95

From Textbook:

``The key is to be sure that the three-way table has a lower percentage of overweight people among the smokers than among the non-smokers. As one example, take 7 smokers with 1 overweight person who dies early (of whom 4 die early). Then take 13 non-smokers with 9 overweight (of whom 3 die early) and 4 not overweight (of whom 1 dies early). Then overall, 4 0f 10 overweight people die early, and 5 of 10 non overweight people die early." (Moore & McCabe, 1998)



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Jonathan Payne
1999-01-26