#1. As a result of chemical pollution, 25 out of the 100 fish caught in the get Sound were inedible. Construct a .98 confidence interval for the true proportion of inedible fish in the Sound.

#2. Suppose a social scientist is interested in estimating the proportion of adults who favor registration of hand guns.

a) How large a sample should be taken, so that he may be 95% confident that the sample proportion will be off by not more than 0.02?

b) Would the sample size be different if the social scientist believes that the proportion favoring registration is not likely to exceed 0.25?

#3. A scientist claims that no more than 10 percent of all persons exposed to certain amount of radiation will feel any ill-effects. If 20 persons are checked, how many will have to feel some ill effects so that the null hypothesis p < .10 can be rejected against the alternate hypothesis p > 0 at the 0.05 level of significance.

#4. There are various ways of testing a random number table for randomness. For instance there should be as many even digits (0,2,4,6 & 8) as there are odd digits (1,3,5,7 & 9). Count the number of the even digits in the first eight rows of the random number table (enclosed), and test at 0.10 level of significance whether, on the basis of this criterion, there is any reason to be concerned about the possibility that the random numbers are not random.

#5. In a random sample of 250 persons who skipped breakfast, 102 reported experiencing midmorning fatigue; and in a random sample of 200 persons who ate breakfast 43 reported that they experienced midmorning fatigue.

a) Compute a 95 percent confidence interval around the true difference between the two proportions.

b) Test at 0.01 level of significance the hypothesis that there is no difference between the corresponding population proportions against the alternate hypothesis that midmorning fatigue is more prevalent among persons who skip breakfast.

c) Same as b) above except that the null hypothesis is P₁ - P₂ = 0.10 and the alternate hypothesis P₁ - P₂ ³ 0.10.

#6. The following sample data pertains to shipments received by a large firm from three different vendors.

Use 0.01 level of significance to test whether the quality of shipments from the three vendors is the same.

#7. Following is the distribution of the time taken by 80 students to do a certain mathematical problem:

Test at .05 level of significance that the data constitutes a random sample from a normal population. The mean and standard deviation of this sample is 20.7 and 5.4 minutes respectively.

#8. The following table shows the number of Douglas fir seedlings counted on a random sample of 400 (2m by 2m) plots in a natural regeneration area.

Test at 0.05 level of significance whether the distribution of seedlings follows POISSON distribution.