Hello,For this question, I've solved (a)(b)(c) subparts.I don't know how to do the rest, which means subparts (d) and (e).Thank you for helping me this. Some of the physiological effects of alcohol are well known. A paper by Squires et al.[1978] assessed the acute effects of alcohol on auditory brainstem potentials in humans.Six volunteers (including the three authors) participated in the study. The latency (delay)in response to an auditory stimulus was measured before and after an intoxicating dose ofalcohol. Seven different peak responses were identified. In this exercise, we discuss onlylatency peak 3. Measurements of the latency of peak (in milliseconds after the stimulusonset) in the six subjects were as follows:Latency of Peak123456.Before alcohol3.853.813.603.683.783.83After alcohol3.823.953.803.873.883.94(a) Test the significance of the difference at the 0.05 level.(b) Calculate the p-value associated with the result observed.(c) Is your p-value based on a one- or two-tailed test? Why?(d) Carry out an (incorrect) two-sample test and state your conclusions.(e) Using the sample variances s? and s associated with the set of readings observedbefore and after, calculate the variance of the difference, assuming independence(call this variance 1). How does this value compare with the variance of thedifference calculated in part (a)? (Call this variance 2.) Why do you supposevariance 1 is so much bigger than variance 2? The average of the differencesis the same as the difference in the averages. Show this. Hence, the two-samplet-test differed from the paired t-test only in the divisor. Which of the two tests inmore powerful in this case, that is, declares a difference significant when in factthere is one?

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Description: Hello,For this question, I've solved (a)(b)(c) subparts.I don't know how to do the rest, which means subparts (d) and (e).Thank you for helping me this. Some of the physiological effects of alcohol are well known. A paper by Squires et al.[1978] asse

Answered: (d) Carry out an (incorrect) two-sample…

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Hello,

For this question, I've solved (a)(b)(c) subparts.

I don't know how to do the rest, which means subparts (d) and (e).

Thank you for helping me this.

Some of the physiological effects of alcohol are well known. A paper by Squires et al.
[1978] assessed the acute effects of alcohol on auditory brainstem potentials in humans.
Six volunteers (including the three authors) participated in the study. The latency (delay)
in response to an auditory stimulus was measured before and after an intoxicating dose of
alcohol. Seven different peak responses were identified. In this exercise, we discuss only
latency peak 3. Measurements of the latency of peak (in milliseconds after the stimulus
onset) in the six subjects were as follows:
Latency of Peak
1
2
3
4
5
6.
Before alcohol
3.85
3.81
3.60
3.68
3.78
3.83
After alcohol
3.82
3.95
3.80
3.87
3.88
3.94
(a) Test the significance of the difference at the 0.05 level.
(b) Calculate the p-value associated with the result observed.
(c) Is your p-value based on a one- or two-tailed test? Why?
(d) Carry out an (incorrect) two-sample test and state your conclusions.
(e) Using the sample variances s? and s associated with the set of readings observed
before and after, calculate the variance of the difference, assuming independence
(call this variance 1). How does this value compare with the variance of the
difference calculated in part (a)? (Call this variance 2.) Why do you suppose
variance 1 is so much bigger than variance 2? The average of the differences
is the same as the difference in the averages. Show this. Hence, the two-sample
t-test differed from the paired t-test only in the divisor. Which of the two tests in
more powerful in this case, that is, declares a difference significant when in fact
there is one?

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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