Stats Exam 1

In a left-tailed test comparing two means with variances unknown but assumed to be equal, the sample sizes were n1 = 8 and n2 = 12. At α = .05, the critical value would be:

-1.734 For d.f. = 18, Appendix D gives t.05 = -1.734.

In a right-tailed test comparing two means with unknown variances assumed to be equal, the sample sizes were n1 = 8 and n2 = 12. At α = .05, the critical value would be:

1.734

John wants to compare two means. His sample statistics were x1=22.7, s1^2=5.4, n1=9 and x2=20.5, s2^2=2.6, n2=9. Assuming equal variances, the test statistic is:

2.20

Which of the following decisions could result in a Type II error for a test?

Fail to reject the null hypothesis

The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm. Which are the hypotheses to test whether the mean is smaller than it is supposed to be?

H0: μ ≥ 56, H1: μ < 56 We want a left-tailed alternative hypothesis.

Which statement about α is not correct?

It is equal to 1 - β.

Which is not true of the two-tailed F-test for equality of variances?

It is fairly robust to the presence of nonnormality in the populations being sampled.

Regarding the probability of Type I error (α) and Type II error (β), which statement is true?

Power = 1 - β

"A study over a 10-year period showed that a certain mammogram test had a 50 percent rate of false positives. This indicates that:" what kind of error is this

This is a 50 percent chance of Type I error.

Rejecting a true null hypothesis is a Type____________________error.

Type 1

An F-test for equality of variances gives a p-value of .003. At α = .05, what conclusion can be made about the preferred test to compare the means for the same sample?

We would not wish to pool the variances in a t-test for equality of means.

The hypothesized value of the mean is..

a target or from past experience

A study over a 10-year period showed that a certain mammogram test had a 50 percent rate of false positives. This indicates that:

about half the tests showed a cancer that didn't exist

The decision rule is:

based on the sampling distribution and chosen level of significance.

Given H0: μ ≥ 18 and H1: μ < 18, we would commit a Type I error if we:

conclude that μ < 18 when the truth is that μ ≥ 18.

The critical value in a hypothesis test:

is a cutoff between the rejection and nonrejection regions

The rejection region in a hypothesis test:

is an area in the tail(s) of a sampling distribution.

A two-tailed hypothesis test:

is used when the direction of the test is of no research interest

There is an inverse relationship between α and β, but...

it is not a simple equation

A medical researcher compared the variances in birth weights for five randomly chosen babies of each gender, with the MegaStat results shown below.

may be assumed equal at any customary α

Simulation studies suggest that the F-test is

robust to modest departures from normality.

The level of significance is not:

the chance of accepting a true null hypothesis.

Reject null hypothesis when...

the p-value is smaller than alpha

In hypothesis testing, the value of β is:

the probability of concluding H0 when H1 is true.

The level of significance is:

the risk of rejecting a true null hypothesis.

In the hypothesis H0: μ = μ0, the value of μ0 is not derived from:

the sample

The decision rule depends on:

the type of test and the level of significance.

A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20, while 16 males had a mean of $17.30 with a standard deviation of $9.60. In comparing the population variances at α = .10 in a two-tailed test, we conclude that:

the variances are unequal.

In a statistical test we:

try to reject the null hypothesis

Assuming unequal variances in a t-test for a zero difference of two means, we would:

use a complicated formula for the degrees of freedom.

The results of the F-test suggest that:

we should assume unequal variances in the t-test

For a right-tailed test with known variances, we would use z.05 = 1.645.

z.05 = 1.645.