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.