Suppose a marketing director of a supermarket chain would like to

     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?