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Chapter 8 Intro to Probability and Statistics

front 1

Assume that a researcher wants to use sample data to test the claim that the sample is from a population with a standard deviation less than 1.8 min. The researcher will use a 0.05 significance level to test that claim. If the researcher wants to use the confidence interval method of testing​ hypotheses, what level of confidence should be used for the confidence​ interval? Will the conclusion based on the confidence interval be the same as the conclusion based on a hypothesis test that uses the​ P-value method or the critical value​ method?

a) If the researcher wants to use the confidence interval method of testing​ hypotheses, what level of confidence should be used for the confidence​ interval?

b) Will the conclusion based on the confidence interval be the same as the conclusion based on a hypothesis test that uses the​ P-value method or the critical value​ method?

back 1

a) Since this is a​ one-tailed test, the researcher should use a confidence level of 0.90.

b)Yes; the confidence interval method and the​ P-value or critical methods always lead to the same conclusion when the tested parameter is the standard deviation.

front 2

Below is when the parameters have the same results

back 2

See Below for Critical Z and P-Value from Z Score and significance for a right tailed test

front 3

Which of the following is NOT a requirement for testing a claim about a standard deviation or​ variance?

a) The population has a normal distribution.

b)The population must be skewed to the right.

c) The sample is a simple random sample.

d) The​ chi-square distribution is used.

back 3

The population must be skewed to the right.

front 4

Which of the following is NOT a property of the​ chi-square distribution?

a) The​ chi-square distribution is different for each number of degrees of​ freedom, df=n-1.

b) The​ chi-square distribution is not symmetric.

c) The mean of the​ chi-square distribution is 0.

d) The values of​ chi-square can be zero or​ positive, but they cannot be negative.

back 4

The mean of the​ chi-square distribution is 0.

front 5

Which of the following is not a requirement for testing a claim about a population with σ not​ known?

a) The value of the population standard deviation is not known.

b) The population​ mean, μ​, is equal to 1.

c) The sample is a simple random sample.

d) Either the population is normally distributed or n>30 or both.

back 5

The population​ mean, μ​, is equal to 1.

front 6

Which of the following is not a characteristic of the t​ test?

a) The Student t distribution has the same general bell shape as the standard normal distribution.

b) The t test is robust against a departure from normality.

c) The Student t distribution is different for different sample sizes.

d) The Student t distribution has a mean of t=0 and a standard deviation of s=1.

back 6

The Student t distribution has a mean of t=0 and a standard deviation of s=1.

front 7

Which of the following is not true when using the confidence interval method for testing a claim about μ when σ is​ unknown?

a) For a​ one-tailed hypothesis test with a 0.05 significance​ level, one must construct a​ 90% confidence interval.

b) The​ P-value method, the traditional​ method, and the confidence interval method are equivalent and yield the same results.

c) For a​ two-tailed hypothesis test with a 0.05 significance​ level, one must construct a​ 95% confidence interval.

d) The​ P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results.

back 7

The​ P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results.

front 8

Which of the following is NOT a requirement for testing a claim about a mean with σ ​known?

a) A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

b) If the sample results​ (or more extreme​ results) cannot easily occur when the null hypothesis is​ true, we explain the discrepancy between the assumption and the sample results by concluding that the assumption is​ true, so we do not reject the assumption.

c) If, under a given​ assumption, there is an exceptionally small probability of getting sample results at least as extreme as the results that were​ obtained, we conclude that the assumption is probably not correct.

d)
If the sample results​ (or more extreme​ results) can easily occur when the null hypothesis is​ true, we attribute the relatively small discrepancy between the assumption and the sample results to chance.

back 8

If the sample results​ (or more extreme​ results) cannot easily occur when the null hypothesis is​ true, we explain the discrepancy between the assumption and the sample results by concluding that the assumption is​ true, so we do not reject the assumption.

front 9

Which of the following is NOT a requirement of testing a claim about a population proportion using a formal method of hypothesis​ testing?

a) The conditions np>5 and nq>5 are both satisfied.

b) The sample observations are a simple random sample.

c) The lowercase​ symbol, p, represents the probability of getting a test statistic at least as extreme as the one representing sample data and is needed to test the claim.

d) The conditions for a binomial distribution are satisfied.

back 9

The lowercase​ symbol, p, represents the probability of getting a test statistic at least as extreme as the one representing sample data and is needed to test the claim.

front 10

Which of the following is NOT true when testing a claim about a​ proportion?

a) If you want to test a claim about population​ proportions, use the​ P-value method or the classical method of hypothesis testing.

b) A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

c) Both the traditional method and​ P-value method use the same standard deviation based on the claimed proportion​ p, but the confidence interval uses an estimated standard deviation based on the sample proportion p-hat.

d) When testing claims about population​ proportions, the traditional method and the​ P-value method are equivalent in the sense that they always yield the same result.

back 10

A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

front 11

​ _____________ is a procedure for testing a claim about a property of a population.

back 11

Hypothesis Test

front 12

Below Solves Z and P Value when X is expressed as a percentage of Sample size

back 12

Continued

front 13

Below Solves Z and P Value when X is expressed as a percentage of Sample size Part 3

back 13

Means Testing Finding T

front 14

The​ _____________ states that​ if, under a given​ assumption, the probability of a particular observed event is extremely​ small, we conclude that the assumption is probably not correct.

back 14

Rare Event Rule

front 15

Which of the following is NOT true of using the binomial probability distribution to test claims about a​ proportion?

a) This method uses the binomial probability distribution with the​ P-value method and uses the value of p assumed in the null hypothesis.

b) In a​ right-tailed test, the​ P-value is the probability of getting x or more successes among the n trials.

c) In a​ left-tailed test, the​ P-value is the probability of getting x or fewer successes among the n trials.

d) One requirement of this method is that np>5 and nq>5.

back 15

One requirement of this method is that np>5 and nq>5.

front 16

P Not Equals

back 16

no data