A psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would like to examine the mean SI score, μ, for the population of all smokers. Previously published studies have indicated that the mean SI score for the population of all smokers is 82and that the standard deviation is 12, but the psychologist believes that the value for the mean has decreased. She plans to perform a statistical test. She takes a random sample of SI scores for smokers and computes the sample mean to be 7.Based on this information, answer the questions below. What are the null hypothesis (H0) and the alternative hypothesis (H1) that should be used for the test? H0: μ is ?less than less than or equal togreater thangreater than or equal to not equal toequal to ? 82 74 12 H1: μ is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ? 82 74 12 In the context of this test, what is a Type II error? A Type II error is ? rejecting/failing to reject the hypothesis that μ is ? less than/less than or equal to greater thangreater than or equal tonot equal toequal to ? 82 74 12 when, in fact, μ is ? less than less than or equal to greater thangreater than or equal to not equal toequal to ? 82 74 12. Suppose that the psychologist decides to reject the null hypothesis. What sort of error might she be making? Type IType II

Name: A psychologist is studying the self image of smokers, as measured by t
Uploaded: 2024-03-20T07:06:16.000Z
Channel: Bartleby
Description: A psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would like to examine the mean SI score, μ, for the population of all smokers. Previously published studies have indicate

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

A psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would like to examine the mean SI score, μ, for the population of all smokers. Previously published studies have indicated that the mean SI score for the population of all smokers is 82and that the standard deviation is 12, but the psychologist believes that the value for the mean has decreased. She plans to perform a statistical test. She takes a random sample of SI scores for smokers and computes the sample mean to be 7.Based on this information, answer the questions below.

What are the null hypothesis (H0) and the alternative hypothesis (H1) that should be used for the test?
H0: μ is ?less than less than or equal togreater thangreater than or equal to not equal toequal to ? 82 74 12

H1: μ is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ? 82 74 12

In the context of this test, what is a Type II error?

A Type II error is ? rejecting/failing to reject the hypothesis that

μ is ? less than/less than or equal to greater thangreater than or equal tonot equal toequal to ? 82 74 12 when, in fact, μ

is ? less than less than or equal to greater thangreater than or equal to not equal toequal to ? 82 74 12.
Suppose that the psychologist decides to reject the null hypothesis. What sort of error might she be making? Type IType II

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 + ...

Expert Solution

Step 1

Solution:

Given information:

$μ = 82 P o p u l a t i o n m e a n σ = 12 P o p u l a t i o n s \tan d a r d d e v i a t i o n s x = 74 S a m p l e m e a n$

Step by step

Solved in 2 steps

Knowledge Booster

$Centre, Spread, and Shape of a Distribution$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions