b) Charles Stevens, the owner of Wilmot Orchards, historically had on average of
ID: 3334732 • Letter: B
Question
b) Charles Stevens, the owner of Wilmot Orchards, historically had on average of 185 apples per tree for his MacIntosh variety. He applies a new fertilizer to his crop and from a random sample of 36 trees, the average yield is 199 apples per tree with a standard deviation of 48 apples per tree. From these data, test the claim at 95% confidence that the fertilizer actually improved his crop yield.
What are the Null and Alternative Hypotheses? (1) I did the Ha as: mean > 185, Ho: mean is < or equal to 185
Prepare the PDF and state the Decision/Rejection Rule for this problem (1, 1) I made it a two tailed test with the Z critical value +1.645
Conduct the test (3) I got Z test value = +1.75
State the Decision and Interpretation (1, 1) because the Z test value is greater than Z critical value, I reject the null hypothesis
What is the Pvalue? (2) the P value is 0.04, thus less than the alpha value, and I reject the Ho
Using this same information, prepare the 95% confidence interval for this new crop. (4) NOW, when I did the confidence interval, I got 185.84 and 212.16 around the mean. However, for the next questions it makes it seem as if the confidence interval should include 185 regardless of whether we rejected the hypothesis… so I’m wondering if it should, and I’ve done something wrong?
Does the 95% confidence interval contain the older average yield (i.e.,185 apples per tree) before the application of this new fertilizer? (1)
If the decision of part i) is to reject the Null Hypothesis, why w/could your confidence interval of part l) include the older average yield of 185 apples per tree? Explain. (2)
Explanation / Answer
what you have done is conduct a one tailed test ;
and when taking confidence interval ; you have taken 2 sided interval ; that is why your results are contradictory,
for a two tailed test ; critical value is 1.96 and p value is 0.08.
If you are testing one tailed test as given in your hypothesis; You should take critical values =1.645 for your confidence interval whcih you might have taken as 1.96.
so in a nutshell you must have same critical value for test and confidence interval if you want your outcomes to be same for both,
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