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?
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.
Below is when the parameters have the same results
See Below for Critical Z and P-Value from Z Score and significance for a right tailed test
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.
The population must be skewed to the right.
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.
The mean of the chi-square distribution is 0.
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.
The population mean, μ, is equal to 1.
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.
The Student t distribution has a mean of t=0 and a standard deviation of s=1.
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.
The P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results.
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.
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.
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.
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.
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.
A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.
_____________ is a procedure for testing a claim about a property of a population.
Hypothesis Test
Below Solves Z and P Value when X is expressed as a percentage of Sample size
Continued
Below Solves Z and P Value when X is expressed as a percentage of Sample size Part 3
Means Testing Finding T
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.
Rare Event Rule
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.
One requirement of this method is that np>5 and nq>5.
P Not Equals
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