Chapter 1. Matched Pairs t Procedures

Correct. Analyzing matched pairs data is the most common use of a one-sample t test.

Incorrect. Analyzing matched pairs data is the most common use of a one-sample t test.

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Correct. When individuals are paired in an experiment, they need to be randomly allocated to the two treatments.

Incorrect. When individuals are paired in an experiment, they need to be randomly allocated to the two treatments.

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Correct. For each pair, we compute the difference between their two measurements.

Incorrect. For each pair, we compute the difference between their two measurements.

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Correct. This is a true statement.

Incorrect. This is a true statement.

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Correct. When two measurements are taken on each individual in an experiment, the order in which the treatments are applied needs to be randomized.

Incorrect. When two measurements are taken on each individual in an experiment, the order in which the treatments are applied needs to be randomized.

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Correct. The one sample of differences from a matched pairs study is analyzed with a one-sample t procedure.

Incorrect. The one sample of differences from a matched pairs study is analyzed with a one-sample t procedure.

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Correct. A difference can be positive, negative or zero.

Incorrect. A difference can be positive, negative or zero.

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Correct. When pre- and post- treatment measurements are taken on each individual, the individuals need to be randomly selected for the study.

Incorrect. When pre- and post- treatment measurements are taken on each individual, the individuals need to be randomly selected for the study.

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Correct. No difference equates to a difference of zero.

Incorrect. No difference equates to a difference of zero.

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Correct. We analyze the differences for each pair when we analyze data for a matched pairs study. This includes plotting the differences and examining the plot for outliers.

Incorrect. We analyze the differences for each pair when we analyze data for a matched pairs study. This includes plotting the differences and examining the plot for outliers.

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Correct. If there is no difference, then the mean of the differences should be zero.

Incorrect. If there is no difference, then the mean of the differences should be zero.

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Correct. If sweetness decreased, then fresh sweetness will be larger than stored sweetness and the mean difference will be greater than zero or H_a: µ_d > 0.

Incorrect. If sweetness decreased, then fresh sweetness will be larger than stored sweetness and the mean difference will be greater than zero or H_a: µ_d > 0.

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Correct. µ_d represents the mean difference. Sweetness is measured and the difference equals fresh minus stored. So µ_d represents the mean difference in sweetness (fresh minus stored).

Incorrect. µ_d represents the mean difference. Sweetness is measured and the difference equals fresh minus stored. So µ_d represents the mean difference in sweetness (fresh minus stored).

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Correct. Because the bottles are paired by belonging to the same batch, they need to be randomly allocated to the two treatments of being tasted fresh or tasted after being stored.

Incorrect. Because the bottles are paired by belonging to the same batch, they need to be randomly allocated to the two treatments of being tasted fresh or tasted after being stored.

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Correct. Differences can be positive, negative or zero. These two differences are not wrong.

Incorrect. Differences can be positive, negative or zero. These two differences are not wrong.

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Correct. s_d = 0.909 is the standard deviation of the differences where each difference is computed as fresh sweetness minus stored sweetness.

Incorrect. s_d = 0.909 is the standard deviation of the differences where each difference is computed as fresh sweetness minus stored sweetness.

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Correct. There are no data points that cause us to say, “Oh, wow!!! That’s an outlier!"

Incorrect. There are no data points that cause us to say, “Oh, wow!!! That’s an outlier!"

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Correct. df = number of differences minus one = 10 – 1 = 9.

Incorrect. df = number of differences minus one = 10 – 1 = 9.

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Correct. With “>” in H_a, the test in one-sided.

Incorrect. With “>” in H_a, the test in one-sided.

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Correct. 0.10 > P-value > 0.05 is greater than α = 0.05, so we should NOT reject H₀.

Incorrect. 0.10 > P-value > 0.05 is greater than α = 0.05, so we should NOT reject H₀.

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Correct. Even though we failed to reject H₀, we do NOT have evidence to say that H₀: µ_d = 0 is correct. Perhaps the sample size of 10 batches is too small to detect significance and we need a larger sample size.

Incorrect. Even though we failed to reject H₀, we do NOT have evidence to say that H₀: µ_d = 0 is correct. Perhaps the sample size of 10 batches is too small to detect significance and we need a larger sample size.

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Correct. Since two incisions were made on the back of each rat and each incision was repaired with a different treatment, this is a matched pairs study.

Incorrect. Since two incisions were made on the back of each rat and each incision was repaired with a different treatment, this is a matched pairs study.

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Correct. P-value = 0.0467 is smaller than α = 0.05, so we reject H₀ and declare the results statistically significant.

Incorrect. P-value = 0.0467 is smaller than α = 0.05, so we reject H₀ and declare the results statistically significant.

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Correct. Since the difference is positive, taped strength is greater than sutured strength.

Incorrect. Since the difference is positive, taped strength is greater than sutured strength.

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Correct. µ_d is the mean difference or the mean of the population of all possible differences.

Incorrect. µ_d is the mean difference or the mean of the population of all possible differences.

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Correct. The parameter is the mean difference in time for all right-handed students where the difference is computed as difference = time to turn counterclockwise knob minus time to turn a clockwise knob.

Incorrect. The parameter is the mean difference in time for all right-handed students where the difference is computed as difference = time to turn counterclockwise knob minus time to turn a clockwise knob.

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Correct. When analyzing matched pairs data, we always plot the differences and check for outliers in the differences.

Incorrect. When analyzing matched pairs data, we always plot the differences and check for outliers in the differences.

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Correct. Since the interval for µ_d, namely (3.87, 22.77), does not contain the value of zero, we can conclude that µ_d is not zero.

Incorrect. Since the interval for µ_d, namely (3.87, 22.77), does not contain the value of zero, we can conclude that µ_d is not zero.

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Correct. Since difference = time to turn a counterclockwise knob minus time to turn a clockwise knob and the entire interval is positive, the average time to turn a counterclockwise knob is greater than the average time to turn a clockwise knob.

Incorrect. Since difference = time to turn a counterclockwise knob minus time to turn a clockwise knob and the entire interval is positive, the average time to turn a counterclockwise knob is greater than the average time to turn a clockwise knob.

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