Chapter 9 Inferences based on two samples
COMPLETION
1. Let be a random sample from a population with mean
be a random sample with mean and that the X and Y samples are independent of one another.
The expected value of is and the standard deviation of = .
ANS:
PTS: 1
2. Let be a random sample from a normal population with mean
be a random sample from a normal population with mean
be a random sample from a normal population with mean
=16, and that X and Y samples are independent of one another. If the sample mean values are
then the value of the test statistic to test is z =
and that will be rejected at .01 significance level if
ANS: -1.45, 2.58, -2.58
PTS: 1
3. In testing the computed value of the test statistic is z = 2.25. The P-value for
this two-tailed test is then .
ANS: .0244
PTS: 1
4. Investigators are often interested in comparing the effects of two different treatments on a response. If the individuals
or subjects to be used in the comparison are not assigned by the investigators to the two treatments, the study is said
to be . If the investigators assign individuals or subjects to the two treatments in a random fashion, this
is referred to as .
ANS: observational, randomized controlled experiment.
PTS: 1
5. Provided that the sample sizes m and n of two independent samples X and Y are both large (i.e., m> 40 and n> 40),
then a confidence interval for the difference between the two population means, with a confidence level of
approximately is , where the values of the population variances are unknown.
ANS:
PTS: 1
,6. Provided that at least one of the sample sizes m and n of two independent samples X and Y is small, and that the
corresponding populations are both normally distributed with unknown values of the population variances, then a
confidence interval for the difference between the two population means, with a confidence level of
is .
, ANS:
PTS: 1
7. The pooled t procedures are alternatives to the two-sample t procedures for situations in which not only the two
population distributions are assumed to be but also they have equal .
ANS: normal, variances
PTS: 1
8. The degrees of freedom associated with the pooled t test, based on sample sizes m and n, is given by .
ANS:
PTS: 1
9. The pooled t confidence interval for estimating with confidence level using two independent
samples X and Y with sizes m and n is given by .
ANS:
PTS: 1
10. The weighted average of the variances of two independent samples is referred to as the of
(the common variance of the two population variances), and is denoted by .
ANS: pooled estimator,
PTS: 1
11. The number of degrees of freedom for a paired t test, where the data consists of n independently pairs
is .
ANS: n-1
PTS: 1
12. The rejection region for level .025 paired t test in testing is , where the
data consists of 12 independent pairs.
ANS:
PTS: 1
13. A 90% confidence interval for the true mean difference in paired data consisting of n independent pairs, is
determined by the formula .
, ANS:
PTS: 1
14. In testing where is the true mean difference in paired data consisting of 16
independent pairs, the value of the test statistic is found to be 2.8. Then the P-value is approximately .
ANS: .014
PTS: 1
15. Let with X and Y independent variables, and let
is an estimator of
ANS: unbiased
PTS: 1
16. In testing denote the two population properties, the P-
value is found to be .0715. Then at .05 level, should .
ANS: not be rejected
PTS: 1
17. In testing denote the two population proportions, the
following summary statistics are given: m = 400, x = 140, n = 500 and y = 160. Then the value of the test statistic is z
= .
ANS: .949
PTS: 1
18. In testing where denote the two population
proportions, the standardized variable is an estimate of the common value of
and m and n are the two sample sizes, has approximately a standard normal distribution when .
ANS: is true
PTS: 1
19. If are independent random variables with degrees of freedom respectively, then
the random variable has an F distribution.
ANS: chi-squared
PTS: 1
COMPLETION
1. Let be a random sample from a population with mean
be a random sample with mean and that the X and Y samples are independent of one another.
The expected value of is and the standard deviation of = .
ANS:
PTS: 1
2. Let be a random sample from a normal population with mean
be a random sample from a normal population with mean
be a random sample from a normal population with mean
=16, and that X and Y samples are independent of one another. If the sample mean values are
then the value of the test statistic to test is z =
and that will be rejected at .01 significance level if
ANS: -1.45, 2.58, -2.58
PTS: 1
3. In testing the computed value of the test statistic is z = 2.25. The P-value for
this two-tailed test is then .
ANS: .0244
PTS: 1
4. Investigators are often interested in comparing the effects of two different treatments on a response. If the individuals
or subjects to be used in the comparison are not assigned by the investigators to the two treatments, the study is said
to be . If the investigators assign individuals or subjects to the two treatments in a random fashion, this
is referred to as .
ANS: observational, randomized controlled experiment.
PTS: 1
5. Provided that the sample sizes m and n of two independent samples X and Y are both large (i.e., m> 40 and n> 40),
then a confidence interval for the difference between the two population means, with a confidence level of
approximately is , where the values of the population variances are unknown.
ANS:
PTS: 1
,6. Provided that at least one of the sample sizes m and n of two independent samples X and Y is small, and that the
corresponding populations are both normally distributed with unknown values of the population variances, then a
confidence interval for the difference between the two population means, with a confidence level of
is .
, ANS:
PTS: 1
7. The pooled t procedures are alternatives to the two-sample t procedures for situations in which not only the two
population distributions are assumed to be but also they have equal .
ANS: normal, variances
PTS: 1
8. The degrees of freedom associated with the pooled t test, based on sample sizes m and n, is given by .
ANS:
PTS: 1
9. The pooled t confidence interval for estimating with confidence level using two independent
samples X and Y with sizes m and n is given by .
ANS:
PTS: 1
10. The weighted average of the variances of two independent samples is referred to as the of
(the common variance of the two population variances), and is denoted by .
ANS: pooled estimator,
PTS: 1
11. The number of degrees of freedom for a paired t test, where the data consists of n independently pairs
is .
ANS: n-1
PTS: 1
12. The rejection region for level .025 paired t test in testing is , where the
data consists of 12 independent pairs.
ANS:
PTS: 1
13. A 90% confidence interval for the true mean difference in paired data consisting of n independent pairs, is
determined by the formula .
, ANS:
PTS: 1
14. In testing where is the true mean difference in paired data consisting of 16
independent pairs, the value of the test statistic is found to be 2.8. Then the P-value is approximately .
ANS: .014
PTS: 1
15. Let with X and Y independent variables, and let
is an estimator of
ANS: unbiased
PTS: 1
16. In testing denote the two population properties, the P-
value is found to be .0715. Then at .05 level, should .
ANS: not be rejected
PTS: 1
17. In testing denote the two population proportions, the
following summary statistics are given: m = 400, x = 140, n = 500 and y = 160. Then the value of the test statistic is z
= .
ANS: .949
PTS: 1
18. In testing where denote the two population
proportions, the standardized variable is an estimate of the common value of
and m and n are the two sample sizes, has approximately a standard normal distribution when .
ANS: is true
PTS: 1
19. If are independent random variables with degrees of freedom respectively, then
the random variable has an F distribution.
ANS: chi-squared
PTS: 1
