- Applications
- General t Distribution Questions
Applications
Methyl Mercury in Mussels
Mierzykowski and Carr (2001) examined the amount of methyl-mercury in freshwater mussels (Elliptio complanata) in four areas in the Sudbury River watershed in Massachusetts. Two of the locations they examined were categorized as reservoirs with one being considered as impacted by the Nyanza Chemical site and the other as not being impacted. The total methyl mercury (in μg meHG per g wet-weight of mussels) for individual mussels sampled from each site is shown below. Use these data to determine if there is a significant difference, at the 5% level, in methyl mercury levels found in mussels between the two locations. Continue with the analysis even if you find that the assumptions have not been met.
impacted 0.011 0.054 0.056 0.095 0.051 0.077 reference 0.031 0.040 0.029 0.066 0.018 0.042 0.044
Popcorn Yield by Variety
A student wanted to determine if the number of unpopped kernels differed between yellow and white varieties of a famous brand of popcorn. To test this, he put 100 kernels of either white or yellow popcorn into a standard air popper, popped the corn until no “pops” were heard, and then counted the number of unpopped kernels. He tested 30 randomly selected groups of 100 kernels for both white and yellow varieties. Use the results below to test, at the 10% level, the student’s hypothesis.
Variable N Mean Median StDev SE Mean
White 30 4.267 2.000 4.456 0.814
Yellow 30 3.567 1.500 4.485 0.819
Levene's Test -- P-Value = 0.972
Heating System Efficiency
A study was performed in order to evaluate the effectiveness of two devices for improving the efficiency of gas home-heating systems. Energy consumption in houses was measured after one of the two devices was installed. The two devices were an electric vent damper (DampVent=Electric) and a thermally activated vent damper (DampVent=ThermAct). Energy consumption (in BTUs) was measured for a variety of houses fitted with the two devices. Compare, at the 10% level, the effectiveness of these two devices by determining if a difference exists in energy consumption between houses fitted with the devices. Note that Levene’s test p-value is 0.996.
DampVent N Mean Median StDev SE Mean Minimum Maximum Q1 Q3
Electric 40 9.908 9.590 3.020 0.477 4.000 18.260 7.885 11.555
ThermAct 50 10.143 10.290 2.767 0.391 2.970 16.060 8.127 12.212
Pork Quality
A pig diet manufacturer wants to determine if the backfat thickness differs between pigs raised on two different diets. Backfat thickness is an indicator of pork quality; smaller thicknesses mean better quality. A group of 24 pigs was randomly allocated to two groups which differed only in the diet received. Test the results from this experiment to see if a difference in backfat thickness (cm) is evident at the 5% level. Note that Levene’s test p-value is 0.532.
Var Diet N Mean Median StDev SE Mean Min Max
BFT 1 12 3.420 3.390 0.295 0.0850 2.87 3.87
2 12 2.989 3.035 0.375 0.108 2.40 3.62
General t Distribution Questions
P-Value Calculations and Decisions
For each situation below, (a) compute the t test statistic, (b) compute the p-value (include a drawing to support your calculation), and (c) make a decision about H0.
- α=0.10, HA: μ1>μ2, n1=12, n2=14, s1=6.6, s2=6.4, x̄1=27.3, and x̄2=23.2.
- α=0.05, HA: μ1<μ2, n1=n2=15, s1=8, s2=9, x̄1=79.5, and x̄2=87.5.
- α=0.05, HA: μ1≠μ2, n1=20, n2=15, s1=56, s2=64, x̄1=307, and x̄2=268.
Confidence Interval Calculations
Compute and interpret confidence regions for the two situations above. You should use the same “steps” as you did in the confidence regions module.