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. 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. Reject Null hypothesis b. Not enough information given to determine the result c. Fail to reject Null hypothesis, given the alternative hypothesis is true d. Fail to reject Null hypthesis e. Fail to reject Null hypothesis, given the null hypothesis is true 2. What is the probability that Alex committed a Type II error?

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. 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. Reject Null hypothesis

b. Not enough information given to determine the result

c. Fail to reject Null hypothesis, given the alternative hypothesis is true

d. Fail to reject Null hypthesis

e. Fail to reject Null hypothesis, given the null hypothesis is true

2. What is the probability that Alex committed a Type II error?

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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