Alex and Ben are two ophthalmologists who are competing for a collaborative grant to perform glaucoma research. The goal of their research is to show that mean daily intraocular pressure (IOP) in subjects with early stage glaucoma is greater than 22 mmHg. Past research has shown that the standard deviation of daily IOP is 2.75 mmHg and that IOP values are normally distributed. Alex and Ben disagree on the significance level that they want to use in their study. Alex wants to use a significance level of 0.02 while Ben wants to use a significance level of 0.06. 1. Assuming that they agree on everything else, whose sample size calculation results in more subjects being recruited for the study? a. It depends on the value of the hypothesized effect size. b. Both will require the same number of subjects. c. Ben’s d. There is not enough information given to determine who will require more subjects. d. Alex’s 2. Alex and Ben collect data from 50 subjects with early stage glaucoma and conduct the hypothesis test of interest using their respective significance levels. Alex rejects the null hypothesis and concludes that the mean daily IOP for subjects with early stage glaucoma is significantly greater than 22 mmHg. If Ben conducts the same hypothesis test, the result would be: a. Fail to reject H0 given H1 true b. Fail to reject H0 c. Reject H0 d. There is not enough information given to determine the result e. Fail to reject H0 given H0 true 3. As noted above, Alex rejects the null hypothesis and concludes that the mean daily IOP for subjects with early stage glaucoma is significantly greater than 22 mmHg. What is the probability that Alex committed a Type II error? a. 0 b. 0.80 c. Either 0 or 1, but we do not know d. 1 e. 0.20

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 14CR

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Alex and Ben are two ophthalmologists who are competing for a collaborative grant to perform glaucoma research. The goal of their research is to show that mean daily intraocular pressure (IOP) in subjects with early stage glaucoma is greater than 22 mmHg. Past research has shown that the standard deviation of daily IOP is 2.75 mmHg and that IOP values are normally distributed.

Alex and Ben disagree on the significance level that they want to use in their study. Alex wants to use a significance level of 0.02 while Ben wants to use a significance level of 0.06.

1. Assuming that they agree on everything else, whose sample size calculation results in more subjects being recruited for the study?

a. It depends on the value of the hypothesized effect size.

b. Both will require the same number of subjects.

c. Ben’s

d. There is not enough information given to determine who will require more subjects.

d. Alex’s

2. Alex and Ben collect data from 50 subjects with early stage glaucoma and conduct the hypothesis test of interest using their respective significance levels. Alex rejects the null hypothesis and concludes that the mean daily IOP for subjects with early stage glaucoma is significantly greater than 22 mmHg. If Ben conducts the same hypothesis test, the result would be:

a. Fail to reject H₀ given H₁ true

b. Fail to reject H₀

c. Reject H₀

d. There is not enough information given to determine the result

e. Fail to reject H₀ given H₀ true

3. As noted above, Alex rejects the null hypothesis and concludes that the mean daily IOP for subjects with early stage glaucoma is significantly greater than 22 mmHg. What is the probability that Alex committed a Type II error?

a. 0

b. 0.80

c. Either 0 or 1, but we do not know

d. 1

e. 0.20

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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