#1. A random sample of 80 cones from a seed orchard gave a mean seed count of 27 with a standard deviation of 4.2.

a) Construct a 90% confidence interval for the true average seed count per cone in the seed orchard.

b) With 99% confidence, what can we say about the maximum difference between the sample mean and the unknown population mean?

#2. The average height of 2 year old seedlings in a nursery is 18 inches. Investigating the option to change the fertilizer composition, the farmer wants to test the null hypothesis µ = 18 inches against a suitable alternative.

a) What null and alternative hypotheses should the owner use if he does not want to make the change unless the new feed is definitely superior.

b) What null and alternative hypotheses should he use if the new feed is cheaper and he would like to use it unless it is definitely inferior.

#3. The yield of sugarbeet from 6 random test plots is 1.4, 1.8, 1.3, 1.9, 2.2 & 1.5 tons per acre. Test at .025 level of significance whether this supports the null hypothesis that the average yield is no more than 1.5 tons per acre.

#4. In a provenence trial, 10 plots of variety A gave an average yield of 2.5 tons with standard deviation of 0.8 ton. 9 plots of variety B, on the other hand, gave an average yield of 3.2 tons with standard deviation of 1.2 tons. Use 0.05 significance level to test if the yield from variety B is greater than the yield from variety A.

#5. A random sample of size 49 is taken from a large population which has standard deviation of 5.6 gm. If we use the mean of this sample to estimate the mean of the population, with what confidence can we assert that the error is not more than 1.2 gm?

#6. In a study of the effectiveness of the weight reduction program, a group of 11 persons engaged in this program for one month showed the following results:

Test at .025 level of significance whether the program is effective in reducing weight

#7. How large a sample would be needed to estimate the average weight of six weeks old chicks within 5% of its true value at 0.95 confidence level.Assume that the coefficient of variation in chick weights is 25%, and that the chick population is extremely large.

Would the sample size be different if N = 1000? Explain.