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49 terms

Chapter 10/11 True/False

STUDY
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A statistical hypothesis is a claim or a statement either about the value of a single population characteristic or about the values of several population characteristics.
True
The statement s squared = 100 is a statistical hypothesis.
False
The null hypothesis is only rejected in favor of the alternative hypothesis when there is convincing evidence against the null hypothesis.
True
The two possible conclusions in a hypothesis test are accept H o and H a.
False
The selection of H o and H a depend on the objectives of the study.
True
If the null hypothesis is not rejected, then there is strong statistical evidence that the null hypothesis is true.
False
A type II error is made by failing to reject a false H o.
True
A type I error is made by rejecting a false H o.
False
Every reasonable test comes with a guarantee that neither a type I nor a type II error will be made.
False
The level of significance of a test is the probability of making a type I error in the test.
True
Choosing a smaller value of alpha will increase the probability of making a type II error.
True
The fundamental idea behind hypothesis testing is to reject H o only when the observed sample is very unlikely to have occurred when H o is true.
True
In a large sample z test for mu, the calculated value of z is the absolute distance between x bar and the true value of mu.
False
The decision to reject or fail to reject H o is based on the value of the test statistic.
True
Small p-values indicate that the observed sample is inconsistent with the null hypothesis.
True
The null hypothesis should be rejected when the p-value is larger than the significance level of the test.
False
It is customary to say that the result of a hypothesis test is statistically significant when the p-value is smaller than alpha.
True
In a large sample z test for p hat, the calculated value of z expresses the distance between p and the hypothesized value as a number of standard deviations.
True
The central limit theorem provides the justification for both the large sample z test and the small sample t test for mu.
False
For testing H o: mu=50 versus H a: mu<50, a calculated z value of -1.98 will have a smaller p-value than would a calculated z value of -1.80.
True
For a two-tailed t test, the p-value for a calculated t value of 2.37 is twice the area to the right of 2.37 on the t curve.
True
The small sample t test for mu should only be used when the population being sampled is approximately normal.
True
Beta is called the observed significance level.
False
When H o is not rejected and beta is large, then there is strong evidence that H o is actually true.
False
For a small sample t test for mu, beta decreases as the sample size increases.
True
Two samples are said to be independent when the selection of the individuals or objects in one sample has no bearing on the selection of those in the other sample.
True
X bar 1 - x bar 2 is an unbiased statistic that can be used to estimate mu 1 - mu 2.
True
For two independent sample, sigma(sub xbar1-xbar2)=sqrt(sigma2,1 over n1 - sigma2,2 over n2).
False
The variance of a difference of two independent quantities is the sum of their individual variances.
True
When the assignment of treatments used in a comparison of treatments is made by the investigators the study is said to observational.
False
In an experiment involving two treatments, rejection of H o: mu1-mu2=0 in favor of H a: mu1-mu2<0 suggests that treatment 2 associates with higher values of the variable to occur.
False
A randomized controlled experiment is particularly useful in suggesting causality.
True
The estimated standard deviation of xbar1-xbar2 used in both the large sample and small sample confidence intervals for mu1-mu2 are the same.
True
The large sample z test for mu1-mu2 can be used as long as at least one of the two sample sizes, n1 and n2, is greater than 30.
False
The two-sample t test for mu1-mu2 should be used when either n1<30 or n2<30.
True
The degrees of freedom of the two-sample t test statistic are based entirely on the values of the sample standard deviations and the sample sizes.
True
The p-value of an upper-tail t test is the area to the right of the calculated t value on the t curve.
True
The degrees of freedom of the two-sample t test statistic are the same as the degrees of freedom for the paired t test statistic.
False
The degrees of freedom used in the two-sample t test are the same as the degrees of freedom used in the two-sample t confidence interval for mu1-mu2.
True
Extraneous factors can sometimes be screened out by using paired samples.
True
H o: mud=2 is equivalent to H o: mu1-mu2=2.
True
xbard can be computed by taking the difference of xbar1 and xbar2.
True
The numerators of the paired t and the two-sample t test statistics are equal.
True
P1-p2 is a biased estimator of phat1-phat2.
False
The standard deviation of p1-p2 used in the large sample test of phat1-phat2 is the same as the standard deviation of p1-p2 used in the large sample confidence interval for phat1-phat2.
False
The paired t test is a distribution-free test.
False
The Mann-Whitney test of mu1-mu2 is a distribution-free test.
True
The test statistic for the rank sum test of mu1-mu2 is the difference of the ranks of the first and second samples.
False
Distribution-free tests of mu1-mu2 can only be used when both n1 and n2 are greater than 30.
False