Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .005 significance level. The null and alternative hypothesis would be: H0:pM≥pFH0:pM≥pF H1:pMμFH1:μM>μF H0:μM=μFH0:μM=μF H1:μM≠μFH1:μM≠μF H0:pM=pFH0:pM=pF H1:pM≠pFH1:pM≠pF H0:pM≤pFH0:pM≤pF H1:pM>pFH1:pM>pF The test is two-tailed right-tailed left-tailed Based on a sample of 80 men, 40% owned cats Based on a sample of 40 women, 70% owned cats Critical Value = [three decimal accuracy] Test Statistic = [three decimal accuracy] Based on this we: Fail to reject the null hypothesis Reject the null hypothesis

Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .005 significance level. The null and alternative hypothesis would be: H0:pM≥pFH0:pM≥pF H1:pMμFH1:μM>μF H0:μM=μFH0:μM=μF H1:μM≠μFH1:μM≠μF H0:pM=pFH0:pM=pF H1:pM≠pFH1:pM≠pF H0:pM≤pFH0:pM≤pF H1:pM>pFH1:pM>pF The test is two-tailed right-tailed left-tailed Based on a sample of 80 men, 40% owned cats Based on a sample of 40 women, 70% owned cats Critical Value = [three decimal accuracy] Test Statistic = [three decimal accuracy] Based on this we: Fail to reject the null hypothesis Reject the null hypothesis

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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Concept explainers

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.

Question

Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .005 significance level.

The null and alternative hypothesis would be:

H0:pM≥pFH0:pM≥pF
H1:pM<pFH1:pM<pF

H0:μM≥μFH0:μM≥μF
H1:μM<μFH1:μM<μF

H0:μM≤μFH0:μM≤μF
H1:μM>μFH1:μM>μF

H0:μM=μFH0:μM=μF
H1:μM≠μFH1:μM≠μF

H0:pM=pFH0:pM=pF
H1:pM≠pFH1:pM≠pF

H0:pM≤pFH0:pM≤pF
H1:pM>pFH1:pM>pF

The test is

two-tailed

right-tailed

left-tailed

Based on a sample of 80 men, 40% owned cats
Based on a sample of 40 women, 70% owned cats

Critical Value =
	[three decimal accuracy]

Test Statistic =
	[three decimal accuracy]

Based on this we:

Fail to reject the null hypothesis
Reject the null hypothesis

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A well-known brokerage firm executive claimed that 80% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 400 people, 72% of them said they are confident of meeting their goals.Test the claim that the proportion of people who are confident is smaller than 80% at the 0.10 significance level.The null and alternative hypothesis would be: H0:p≤0.8H0:p≤0.8 H1:p>0.8H1:p>0.8 H0:μ=0.8H0:μ=0.8 1:μ≠0.8H1:μ≠0.8 H0:μ≤0.8H0:μ≤0.8 H1:μ>0.8H1:μ>0.8H0:p=0.8H0:p=0.8H1:p≠0.8H1:p≠0.8 H0:p≥0.8H0:p≥0.8 H1:p<0.8H1:p<0.8 H0:μ≥0.8H0:μ≥0.8 H1:μ<0.8H1:μ<0.8 The test is: left-tailed right-tailed two-tailed The test statistic is: __?___ (to 3 decimals)The p-value is: __?___ (to 4 decimals)
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