b)Does vigorous exercise affect concentration? In general, the time needed for people to complete a certain paper-and-pencil maze follows a normal distribution, with a mean of 30 seconds and a standard deviation of three seconds. You wish to see if the mean time is changed by vigorous exercise, so you have a random sample of nine employees of your company (who you assume are representative of people in general) exercise vigorously for 30 minutes and then complete the maze. You compute the mean of their times to complete the maze and use this information to test the hypotheses at the 1% significance level. Rounded to 3 decimal places, the critical values of the sample mean are ______ Multiple Choice + 2.575 and - 2.575 27.674 and 32.326 27.425 and 32.575 cannot be determined without knowing the sample mean - 2.33 and +2. 33 -3.355 and + 3.355 c)The average property size in the rural part of some town is believed to be 10 acres. A random sample of 16 properties reveals a mean size of 12 acres. Assume that the population standard deviation is known to be 4 acres, and that the number of acres per property is normally distributed. The p-value for conducting a hypothesis test to determine if the mean property size is likely to be 10 acres will be which of the following? 0.0228 0.6170 0.0456 0.9772

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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b)Does vigorous exercise affect concentration? In general, the time needed for people to complete a certain paper-and-pencil maze follows a normal distribution, with a mean of 30 seconds and a standard deviation of three seconds. You wish to see if the mean time is changed by vigorous exercise, so you have a random sample of nine employees of your company (who you assume are representative of people in general) exercise vigorously for 30 minutes and then complete the maze. You compute the mean of their times to complete the maze and use this information to test the hypotheses at the 1% significance level. Rounded to 3 decimal places, the critical values of the sample mean are ______

Multiple Choice

+ 2.575 and - 2.575
27.674 and 32.326
27.425 and 32.575
cannot be determined without knowing the sample mean
- 2.33 and +2. 33
-3.355 and + 3.355

c)The average property size in the rural part of some town is believed to be 10 acres. A random sample of 16 properties reveals a mean size of 12 acres. Assume that the population standard deviation is known to be 4 acres, and that the number of acres per property is normally distributed. The p-value for conducting a hypothesis test to determine if the mean property size is likely to be 10 acres will be which of the following?

0.0228
0.6170
0.0456
0.9772

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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