A researcher wishes to determine if students are able to complete a certain puzzle more quickly while exposed to a pleasant floral scent. Suppose the time (in seconds) needed for high school students to complete the puzzle while exposed to the scent follows a normal distribution with mean m and standard deviation s = 4. Suppose also, that in the general population of all high school students, the time needed to complete the puzzle follows a normal distribution with mean 80 and standard deviation s = 4. The researcher, therefore, decides to test the hypotheses H0: m = 80 Ha: m < 80. To do so, the researcher has 10,000 high school students complete the puzzle in the presence of the floral scent. The mean time for these students is = 80.2 seconds and the P-value is less than 0.0001. 1. It is appropriate to conclude which of the following? A) The researcher has proved that for high school students a pleasant floral scent substantially improves the time it takes to complete the puzzle. B) The researcher has strong evidence that for high school students a pleasant floral scent improves the time it takes to complete the puzzle. C) The researcher has moderate evidence that for high school students a pleasant floral scent substantially improves the time it takes to complete the puzzle. D) None of the above. With such a large sample size, statistically significant results may not be of any practical importance.

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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A researcher wishes to determine if students are able to complete a certain puzzle more quickly while exposed to a pleasant floral scent. Suppose the time (in seconds) needed for high school students to complete the puzzle while exposed to the scent follows a normal distribution with mean m and standard deviation s = 4. Suppose also, that in the general population of all high school students, the time needed to complete the puzzle follows a normal distribution with mean 80 and standard deviation s = 4. The researcher, therefore, decides to test the hypotheses

H₀: m = 80 H_a: m < 80.

To do so, the researcher has 10,000 high school students complete the puzzle in the presence of the floral scent. The mean time for these students is = 80.2 seconds and the P-value is less than 0.0001.

1.	It is appropriate to conclude which of the following?
	A)	The researcher has proved that for high school students a pleasant floral scent substantially improves the time it takes to complete the puzzle.
	B)	The researcher has strong evidence that for high school students a pleasant floral scent improves the time it takes to complete the puzzle.
	C)	The researcher has moderate evidence that for high school students a pleasant floral scent substantially improves the time it takes to complete the puzzle.
	D)	None of the above. With such a large sample size, statistically significant results may not be of any practical importance.

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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