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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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