Chapter 10/11 True/False

A type I error is made by rejecting a false H o.

False

Beta is called the observed significance level.

False

Distribution-free tests of mu1-mu2 can only be used when both n1 and n2 are greater than 30.

False

Every reasonable test comes with a guarantee that neither a type I nor a type II error will be made.

False

For two independent sample, sigma(sub xbar1-xbar2)=sqrt(sigma2,1 over n1 - sigma2,2 over n2).

False

If the null hypothesis is not rejected, then there is strong statistical evidence that the null hypothesis is true.

False

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

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

P1-p2 is a biased estimator of phat1-phat2.

False

The central limit theorem provides the justification for both the large sample z test and the small sample t test for mu.

False

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 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 null hypothesis should be rejected when the p-value is larger than the significance level of the test.

False

The paired t test is a distribution-free test.

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 statement s squared = 100 is a statistical hypothesis.

False

The test statistic for the rank sum test of mu1-mu2 is the difference of the ranks of the first and second samples.

False

The two possible conclusions in a hypothesis test are accept H o and H a.

False

When H o is not rejected and beta is large, then there is strong evidence that H o is actually true.

False

When the assignment of treatments used in a comparison of treatments is made by the investigators the study is said to observational.

False

A randomized controlled experiment is particularly useful in suggesting causality.

True

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

A type II error is made by failing to reject a false H o.

True

Choosing a smaller value of alpha will increase the probability of making a type II error.

True

Extraneous factors can sometimes be screened out by using paired samples.

True

For a small sample t test for mu, beta decreases as the sample size increases.

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

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

H o: mud=2 is equivalent to H o: mu1-mu2=2.

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

It is customary to say that the result of a hypothesis test is statistically significant when the p-value is smaller than alpha.

True

Small p-values indicate that the observed sample is inconsistent with the null hypothesis.

True

The Mann-Whitney test of mu1-mu2 is a distribution-free test.

True

The decision to reject or fail to reject H o is based on the value of the test statistic.

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 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

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 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

The level of significance of a test is the probability of making a type I error in the test.

True

The null hypothesis is only rejected in favor of the alternative hypothesis when there is convincing evidence against the null hypothesis.

True

The numerators of the paired t and the two-sample t test statistics are equal.

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 selection of H o and H a depend on the objectives of the study.

True

The small sample t test for mu should only be used when the population being sampled is approximately normal.

True

The two-sample t test for mu1-mu2 should be used when either n1<30 or n2<30.

True

The variance of a difference of two independent quantities is the sum of their individual variances.

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

xbard can be computed by taking the difference of xbar1 and xbar2.

True