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In a study on the fertility of married women conducted by Martin O'Connell and Carolyn C. Rogers for the Census Bureau in 1979 , two groups of childless wives aged 25 to 29 were selected at random and each wife was asked if she eventually planned to have a child. One group was selected from among those wives married less than two years and the other from among those wives married five years. Suppose that 240 of 300 wives married less than two years planned to have children some day compared to 288 of the 400 wives married five years, Can we conclude that the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years? Make use of a P-value

An urban community would like to show that the incidence of breast cancer is higher than in a nearbyrural area. (PCB levels were found to be higher in the soil of the urban community.) If it is found that 20 of 200 adult women in the urban community have breast cancer and 10 of 150 adult women in the rural commus nity have breast cancer, can we conclude at the 0.05 level of significance that breast cancer is more prevalent in the urban community?

The hydrocarbon emissions are known to have decreased dramatically during the 1980 s. A study was conducted to compare the hydrocarbon emissions at idling speed, in parts per million (ppm), for automobiles of 1980 and \(1990 .\) Twenty cars of each year model were randomly selected and their hydrocarbon emission leycls were recorded. The data are as follows 1980 models: \(\begin{array}{llllllllll}141 & 359 & 247 & 940 & 882 & 494 & 306 & 210 & 105 & 880 \\ 200 & 223 & 188 & 940 & 241 & 190 & 300 & 435 & 241 & 380\end{array}\) 1990 models: \(\begin{array}{rrrrrrrrrr}140 & 160 & 20 & 20 & 223 & 60 & 20 & 95 & 360 & 70 \\\ 220 & 400 & 217 & 58 & 235 & 380 & 200 & 175 & 85 & 65\end{array}\) Test the hypothesis that \(\sigma_{1}=\sigma_{2}\) against the alternative that \(\sigma_{1} \neq \sigma_{2}\). Assume both populations are normal. Use a P-value.

A die is tossed 180 times with the following results: \begin{tabular}{c|cccccc} \(x\) & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \(\boldsymbol{f}\) & 28 & 36 & 36 & 30 & 27 & 23 \end{tabular} Is this a halanced die? Use a 0.01 level of significance.

\( \quad \wedge\) machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5: 2: 2: 1 . A can containing 500 of these mixed nuts was found to have 269 peanuts, 112 hazelnuts, 74 cashews, and 45 pecans. At the 0.05 level of significance, test the hypothesis that the machine is mixing the nuts in the ratio \(5: 2 ; 2: 1\).

The grades in a statistics course for a particular semester were as follows: \begin{tabular}{l|lllll} Grade & \(\mathrm{A}\) & \(\mathrm{B}\) & \(\mathrm{C}\) & \(\mathrm{D}\) & \(\mathrm{F}\) \\ \hline\(/\) & 14 & 18 & 32 & 20 & 16 \end{tabular} Test the hypothesis, at the 0.05 level of significance, that the distribution of grades is uniform.

In Exercise 1.19 on page \(28,\) test the goodness of fit between the observed class frequencies and the corresponding expected frequencies of a normal distribution with \(p=1.8\) and \(a=0.4,\) using a 0.01 level of significance.

In an experiment to study the dependence of hypertension on smoking habits, the following data were taken on 180 individuals Test the hypothesis that the presence or absence of hy pertension is independent of smoking habits. Use 0.05 level of significance.

State the null and alternative hypotheses to be used in testing the following claims and determine generally where the critical region is located: (a) The mean snowfall at Lake George during the month of February is 21.8 centimeters. (b) No more than \(20 \%\) of the faculty at the local university contributed to the annual giving fund. (c) On the average, children attend schools within 6.2 kilometers of their homes in suburban St. Louis. (d) At least \(70 \%\) of next year's new cars will be in the compact and subcompact category. (e) The proportion of voters favoring the incumbent in the upcoming election is 0.58 . (f) The average rib-eye steak at the I.onghorn Steak house is at least 340 grams.

State the null and alternative hypotheses to be used in testing the following claims, and determine generally where the critical region is located: (a) At most, \(20 \%\) of next year's whent crop will be exported to the Soviet Union. (b) On the average, American homemakers drink 3 cups of coffee per day (c) The proportion of graduates in Virginia this year majoring in the social sciences is at least. \(0.15 .\) (d) The average donation to the American Lung Association is no more than \(\$ 10\). (e) Residents in suburban Richmond commute, on the average, 15 kilometers to their place of employment.