Statistics / Mr. Hansen 3/11/2004

Check one:

Name: __________________________________ c Regular time (36 minutes) c Extended time (54 minutes)

Test on Chapters 11 and 12

Instructions and Scoring.

• Show all work and answers on separate sheets.
• Show as much work as time provides. Justify all steps except for algebraic simplification or z or t area calculations. The calculation of the value of z or t should be shown. Also, for full credit, you should show the details of s.e. and m.o.e. calculations to the extent possible.
• You will not earn full credit for a correct answer without adequate justification, or a correct answer without correct notation.

	The 4-H organization is a large nationwide club for young people interested in agriculture. An SRS of 55 members from all across the United States is recruited to see which of two fertilizers is more effective in the raising of green beans. Each 4-H member is instructed to create a garden plot of a certain square footage (the same for each participant) and then divide that plot into two equal parts. The members are then to flip a coin to decide which subplot of their garden will receive fertilizer A and which will receive fertilizer B. At the end of the growing season, the 4-H members are to weigh the beans from each plot and report their findings to the central office. The test administrators at 4-H national headquarters speculate that fertilizer A is, in fact, more effective.
1.	Does the design incorporate blinding? Speculate briefly (2-3 sentences) on how the blinding should be carried out.
2.	The “A” plots have a mean yield of 120 lbs. of beans with a sample s.d. of 6 lbs. The “B” plots have a mean yield of 114 lbs. with a sample s.d. of 5 lbs. The differences in yields (B – A) have a mean of –6 lbs. with a sample s.d. of 3.5 lbs. Is there evidence to support the hypothesis of the people at 4-H headquarters?
3.	If both sets of results are normally distributed, compute the probability that a randomly selected “A” plot (from any of the students) is more productive than a randomly selected “B” plot (from any of the students).
4.	Among the 55 students are 28 boys and 27 girls. Among the boys, 75% think that George W. Bush is articulate, but only 2/3 of the girls feel that way. Develop a 90% confidence interval for the difference between the proportion of boys and girls who think that George W. Bush is articulate.
5.	Is there evidence at the 5% significance level to support the claim of a difference between the percentage of male 4-H members and female 4-H members who think that George W. Bush is articulate?