Does drying barley seeds in a kiln increase the yield of barley? A famous experiment by William S. Gosset (who discovered the distributions) investigated this question. Eleven pairs of adjacent plots were marked out in a large t field. For each pair, regular barley seeds were planted in one plot and kiln-dried seeds were planted in the other. The following table displays the data on yield (lb/acre). (a) How can the Random condition be satisfied in this study? (b) Perform an appropriate test to help answer the research question. Assume that the Random condition is met. What conclusion would you draw? Correct Answer (a) By randomly allocating which plot got the regular barley seeds and which one got the kiln-dried seeds. (b) State: We want to perform a test of = 0 versus < 0, where is the actual mean difference (regular kiln) in H0: μd Ha: μd μd − yield between regular barley seeds and kiln-dried barley seeds. We will perform the test at the = 0.05 significance α level. Plan: If conditions are met, we should do a paired test for the population mean We are told that t Random: μ. this was a randomized experiment. The sample size was 11, so we check a graph. The histogram below Normal: shows no strong skewness or outliers in the data. There were 11 pairs of plots used in the sample. This is Independent: clearly less than 10% of all possible plots. All conditions have been met. Do: The sample mean and standard deviation are and = 66.2. The corresponding test statistic is = The sx t −1.688. from technology using df = 10 is 0.0612. Since our is greater than 0.05, we fail to reject the Conclude: P-value null hypothesis. We do not have enough evidence to conclude that kiln-dried barley seeds produce a larger yield.
Does drying barley seeds in a kiln increase the yield of barley? A famous experiment by William S. Gosset (who discovered the t distributions) investigated this question. Eleven pairs of adjacent plots were marked out in a large field. For each pair, regular barley seeds were planted in one plot and kiln-dried seeds were planted in the other. The following table displays the data on yield (lb/acre). (a) How can the Random condition be satisfied in this study? (b) Perform an appropriate test to help answer the research question. Assume that the Random condition is met. What conclusion would you draw? Correct Answer (a) By randomly allocating which plot got the regular barley seeds and which one got the kiln-dried seeds. (b) State: We want to perform a test of H0: μd = 0 versus Ha: μd < 0, where μd is the actual mean difference (regular − kiln) in yield between regular barley seeds and kiln-dried barley seeds. We will perform the test at the α = 0.05 significance level. Plan: If conditions are met, we should do a paired t test for the population mean μ. Random: We are told that this was a randomized experiment. Normal: The sample size was 11, so we check a graph. The histogram below shows no strong skewness or outliers in the data. Independent: There were 11 pairs of plots used in the sample. This is clearly less than 10% of all possible plots. All conditions have been met. Do: The sample mean and standard deviation are and sx = 66.2. The corresponding test statistic is t = −1.688. The from technology using df = 10 is 0.0612. Conclude: Since our P-value is greater than 0.05, we fail to reject the null hypothesis. We do not have enough evidence to conclude that kiln-dried barley seeds produce a larger yield.
chapter_9_review_and_questions.docx