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After hearing that students can improve short-term memory by chewing the same flavor of gum while studying for and taking a test, Leila and Valerie designed an experiment to investigate. Using 30 volunteers, they randomly assigned 15 to chew gum while they studied a list of 40 words for 90 seconds. Immediately after the 90-second study period—and while chewing the same gum—the subjects wrote down as many words as they could remember. The remaining 15 followed the same procedure without chewing gum. Two weeks later, each of the 30 subjects did the opposite treatment. The number of words correctly remembered for each test was recorded for each subject.
The 95% confidence interval for the true mean difference (gum – no gum) in number of words remembered is –0.67 to 1.54. Interpret the confidence level.
If Leila and Valerie were to (repeat this experiment or select a random sample) many times with these 30 volunteers and construct a 95% confidence interval using (each random sample or the results of each experiment) , about 95% of the intervals would (capture the true mean difference or contain the sample mean difference) (gum – no gum) in the number of words remembered for (students like these or all subjects)
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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