Below are the specific instructions for assignment #4. This assignment can be submitted in pencil and paper form, Word, or scanned and sent to me in pdf format. You can use Excel or a plain old calculator to perform the calculations. You must show your work (i.e. the formulas that you used) on paper! You will get no credit for just giving the answer without supporting your work.

A farmer in Arizona is considering two different rootstocks (A and B) for grapefruit trees. He is also considering the effects of a new chemical treatment to be applied to rootstock A. The farmer uses a small test plot and plants 6 trees using rootstock \(\mathrm{A}\) and 5 trees using rootstock B. After 5 years when the fruit is ripe, he adds up the number of oranges on each tree and tabulates the results in the table below. After that is done, he treats rootstock A with a new chemical, waits until the next harvest, and records the new yield for rootstock A associated with the new chemical treatment in the last column of the table below.

Table 1: Non-Proportions (Used for Questions 1-3)

1. Assuming that the yield of rootstock A (untreated) is normally distributed, use the test for the mean of a small sample (formula 9.2) to test the hypothesis that the population mean yield is less than 200 grapefruit per tree at a \(95 \%\) level of significance.
2. Assuming that the yield of rootstock A and B (untreated) are both normally distributed, use the pooled variance t-test for the difference between two means for small independent samples (formula 10.2) to test the hypothesis that the population mean yield for rootstock A and rootstock B are equal. Use a \(99 \%\) level of significance.
3. Assuming that the yield of rootstock A both treated and untreated are both normally distributed, use the paired t-test for the mean difference in two small dependent samples (formula 10.5) to test the hypothesis that the population mean yield for rootstock A is equal regardless of whether it is treated or not. Use a \(99 \%\) level of significance.
   Consumers in two different states were asked to try a new soft drink and say whether they liked it or disliked it. The results are summarized in the following contingency table:
   Table 2: Proportions (Used for Questions 4-5)
   
4. Using the Z-test of a hypothesis for one proportion (formula 9.3), test to see if the population mean proportion of Arizona customers that liked the new soft drink is equal to \(60 \%\) using a significance level \(99 \%\). What is the P-value associated with this test?
5. Using the Z-test for the difference between two proportions (formula 10.7), test to see if the population mean proportion of customers that liked the new soft drink in Arizona is equal to the mean proportion of customers that liked the new soft drink in California. Use a \(95 \%\) level of significance.
   Three different types of wheat seed were tested in a greenhouse and the yield (bushels per acre) was recorded for each. In the greenhouse, 4 sub-plots of seed type 1 were planted, 2 sub-plots of seed type 2 were planted, and 3 sub-plots of seed type 3 were planted.
   Table 3: Yields (Used for Questions 6-7)
   
6. Using the F-test statistic for comparing two variances (formula 10.9) determine if the variances of seed type 1 and seed type 2 are significantly different from each other at a \(90 \%\) level of significance.
7. Using the one-way ANOVA F-test statistic (formula 10.15) test the hypothesis that the yield of all three seed types is equal at a \(95 \%\) level of significance.

Price: $16.63

Solution: The downloadable solution consists of 7 pages, 963 words and 3 charts.
Deliverable: Word Document