1. Suppose a marketing director of a supermarket chain would like to estimate the population-mean sales of a new cereal within +/- $25 with 95% confidence. If the population standard deviation is assumed to be $150, what sample size is needed? What would be your sample size if your population is 3000?
2. An agronomist wants to compare the crop yield of three varieties of chickpea seeds. She plants 15 fields, five with each variety. She then measures the crop yield in bushels per acre. The results are presented in the following table: Seed 1 Seed 2 Seed 3 11.1 13.5 15.3 14.6 9.8 19.0 18 19.8 19.6 16.6 14.6 15.7 16.8 16.7 15.2 a) Run a single factor ANOVA in Excel and give the ANOVA table. b) test for the equality of mean crop yields of the three different seeds at 0.01significance level and include your null and alternative hypothesis. c) What is the p-value for this test? Explain the meaning of the p-value.
3. The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm is related to the sales generated by the broker. They sample 6 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows: No. of Clients Sales 27 11 42 33 15 25 52 37 64 55 29 58 a) Plot the data. b) What is the standard error for your predictions? What does it mean?