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Description: Many studies have been conducted to test the effects of marijuana use on mental abilities. In one such study, groups of light and heavy users of marijuana in college were tested for memory recall, with the results given below. Use a a 0.05 signific

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Many studies have been conducted to test the effects of marijuana use on mental abilities. In one such study, groups of light and heavy users of marijuana in college were tested for memory recall, with the results given below. Use a a 0.05 significance level to test the claim that in the population of heavy marijuana users, the mean number of items sorted correctly is lower than the mean number in the population of light users.

Items sorted correctly by light marijuan users: n = 64,

x overbar equals

53.5

s = 3.6

Items sorted correctly by heavy marijuan users: n = 65,

x overbar equals

51.8

s = 4.5

a. Define the parameters

mu 1 equals

The mean number of light marijuana users

mu 2 equals

The mean number of heavy marijuan users

p 1 equals

The proportion of light marijuana users

p 2 equals

The proportion of heavy marijuana users

p 1 equals

The proportion of items sorted correctly by all light marijuana users

p 2 equals

The proportion of items sorted correctly by all heavy marijuana users

mu 1 equals

The mean number of items sorted correctly by all light marijuana users

mu 2 equals

The mean number of items sorted correctly by all heavy marijuana users

b. State the null and alternative hypotheses

Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 greater than mu 2

Upper H 0 : mu 1 equals

53.5

Upper H 1 : mu 2 equals

51.8

Upper H 0 : p 1 equals p 2 Upper H 1 : p 1 greater than p 2

Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 less than mu 2

c. Calculate the P-value. Which of these options is closest to its value?

0.0088

0.0110

0.0132

0.0096

d. State the technical conclusion

Reject Upper H 0

Do not reject Upper H 0

e. State the final conclusion

The sample data support the claim.

There is not sufficient evidence to warrant rejection of the claim.

There is sufficient evidence to warrant rejection of the claim.

There is not sufficient sample evidence to support the claim.

f. Should marijuana use be of concern to students?

Yes

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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