Question

Problem: A company is claiming that their new product BrawndoTM is “what the plants crave”. As the sole researcher left in the country, you are skeptical and worried that BrawndoTM may have too many electrolytes for plants and actually hurts crops. You test whether BrawndoTM hurts crop yield. Since this is such an important decision, you want to be conservative and use a significance test of p=.01 before making any conclusions. You know that using the traditional water method led to an average yield of 40 bushels of wheat, with a standard deviation of 7 bushels. You test BrawndoTM on a hundred (100) randomly selected acres of wheat and find that the average yield for this sample is 38 bushels of wheat.

Show all work to (including drawing/shading distributions where appropriate). Round all steps/answers to 2 decimal places.

1. Restate the question:

   • Population 1:

   • Population 2:

   • Research hypothesis:

   • Null hypothesis:

   • Determine the characteristics of the comparison distribution to compare to sample distribution:

     • μ1 (Population 1, sample):

     • N (Population 1, sample):

     • μ2 (Population 2, entire population):

     • σ2(Population 2, entire population):

     • μ2M (Population 2, distribution of means)

     • σ2M (Population 2, distribution of means):

     • Is the distribution of means normally distributed?

     • Why does the distribution of means have a normal distribution, a non-normal distribution, or an unknown distribution?

     • c. Determine the critical value on the comparison distribution at which the null hypothesis should be rejected.

     • Determine the Z score of your sample

     • Decide whether to reject the null hypothesis

     • The president asks for a summary of what you found, describe the findings to a non-scientist:

     • BrawndoTM representatives are claiming that the 100 acres you selected for your study just happened to be poor acres of land and if you re-run your study using BrawndoTM on a new sample of 100 acres of that the yield will be much higher than the average of 38 bushels you found from your sample. What is the range of values where you would be 95% confident the average of the new sample of 100 would lie within (95% confidence interval)?

Answer 1

The hypothesis being tested is:

H0: µ = 40

Ha: µ ≠ 40

40.00	hypothesized value
38.00	mean 1
7.00	std. dev.
0.70	std. error
100	n
-2.86	z
.0043	p-value (two-tailed)
36.63	confidence interval 95.% lower
39.37	confidence interval 95.% upper
1.37	margin of error

The z-score is -2.86.

The critical value is 1.96.

Since the p-value (0.0043) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that using the traditional water method led to an average yield of 40 bushels of wheat.

The 95% confidence interval for the average of the new sample of 100 would lie within 36.63 and 39.37.