An agricultural field trial compares the yield of two varieties of tomatoes for commercial use. The researchers divide in half each of 10 small plots of land in different locations and plant each tomato variety on one half of each plot. After harvest, they compare the yields in pounds per plant at each location. The 10 differences (Variety A – Variety B) give and . Is there convincing evidence that Variety A has the higher mean yield?

a) Describe what the parameter ì is in this setting.

b) State H0 and Ha.

c) Find the appropriate test statistic and P-value. What do you conclude? (Do not just say accept or reject H0. Say what you mean in context.)

I'll give you some hints to get started, then let you take it from there.

You may be able to use a two-sample independent groups t-test for your data.
Ho: µA = µB (A = Variety A; B = Variety B)
Ha: µA > µB

The P-value is the actual level of the test statistic. Once you calculate the observed t-value from the formula, you can then determine the p-value using a t-table.

Remember that a test is only statistically significant if the null hypothesis (Ho) is rejected.

a) In this setting, the parameter μ represents the mean yield of the two varieties of tomatoes for commercial use.

b) H0: μA = μB (There is no difference in the mean yield between Variety A and Variety B)
Ha: μA > μB (Variety A has a higher mean yield than Variety B)

c) To test this hypothesis, we can use a two-sample independent groups t-test.

The appropriate test statistic for a two-sample independent groups t-test is calculated by using the formula:

t = (x̄A - x̄B) / √[(sA^2/nA) + (sB^2/nB)]

where x̄A is the mean yield for Variety A, x̄B is the mean yield for Variety B, sA and sB are the sample standard deviations for Variety A and Variety B respectively, nA is the sample size for Variety A, and nB is the sample size for Variety B.

The p-value is the probability of observing a test statistic as extreme as the observed t-value, assuming the null hypothesis is true. We can find the p-value by referring to a t-table using the degrees of freedom (df) for the test.

To conclude, we would compare the p-value to a predetermined significance level (α) to make a decision. If the p-value is less than α, we would reject the null hypothesis and conclude that there is convincing evidence that Variety A has a higher mean yield. If the p-value is greater than or equal to α, we would fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that Variety A has a higher mean yield.