Question 1

If we are testing the hypothesis about the mean of a population of paired differences with samples of n₁ = 10,n₂ = 10,the degrees of freedom for the t statistic is ____. A)20 B)9 C)18 D)10

Accepted Answer

The degrees of freedom for a paired t-test is given by df = n - 1, where n is the number of pairs. In this case, we have 10 pairs in each sample, so the degrees of freedom for the t statistic is df = 10 - 1 = 9. Therefore, the correct choice is B.

Question 2

In general,the shape of the F distribution is _________.
A)skewed right
B)skewed left
C)normal
D)binomial

Accepted Answer

The F distribution is skewed right due to the fact that values cannot be negative and as the degrees of freedom for the numerator increase, the distribution becomes increasingly skewed in the positive direction.

Question 3

In testing the difference between two independent population means,it is assumed that the level of measurement is at least ______________.
A)a ratio variable
B)a qualitative variable
C)an interval variable
D)a categorical variable

Accepted Answer

In testing the difference between two independent population means, it is assumed that the level of measurement is at least an interval variable. Interval variables have equal intervals between values but have no true zero point. This is necessary for calculating meaningful differences between means. Ratio variables have a true zero point, but this level of measurement is not necessary for testing the difference between two independent population means. Qualitative and categorical variables do not have numerical or quantitative values, so they cannot be used to measure mean differences.

Question 4

An experiment in which two different measurements are taken on the same units and inferences are made using the differences between the pairs of measurements is a(n)______ experiment.
A)Paired difference
B)Equal variances
C)Independent samples
D)Dependent samples

Accepted Answer

A paired difference experiment is the only option listed that involves two different measurements taken on the same units, which is the key characteristic of this type of experiment. In this type of experiment, the differences between the pairs of measurements are analyzed to draw inferences. The other options listed do not involve two different measurements taken on the same units.

Question 5

When comparing two independent population means when population variances are not known and the samples are normally distributed,the correct test statistic to use is ____. A)Z B)t C)F D)t²

Accepted Answer

When comparing two independent population means with unknown variances and normally distributed samples, we use the two-sample t-test. Therefore, the correct test statistic to use is t.

Question 6

Given the following information about a hypothesis test of the difference between two variances based on independent random samples,what is the critical value of the test statistic at a significance level of .05? Assume that the samples are obtained from normally distributed populations. H_A: $\sigma$²_A> $\sigma$²_B, ₁ = 12, ₂ = 9,s₁ = 5,s₂ = 3,n₁ = 13,n₂ = 10. A)3.87 B)3.44 C)3.07 D)2.8 E)2.38

Accepted Answer

The answer of Given the following information about a hypothesis...

Question 7

When comparing two independent population variances,the correct test statistic to use is __________. A)Z B)t C)F D)t²

Accepted Answer

The correct test statistic to use when comparing two independent population variances is the F-test. The F-test compares the ratio of variances between two populations to determine if they are significantly different.

Question 8

An experiment in which there is no relationship between the measurements on the different samples is a(n)______ experiment.
A)Paired difference
B)Equal variances
C)Independent samples
D)Dependent samples

Accepted Answer

Independent samples refer to samples that are not related or dependent on each other. Therefore, if there is no relationship between the measurements on the different samples, it is an independent samples experiment. Paired difference experiments involve two related samples, equal variances experiments involve comparing variances between two samples, and dependent samples experiments involve samples that are related or dependent on each other.

Question 9

The test of means for two related populations match the observations (matched pairs)in order to reduce the ________________ attributable to the difference between individual observations and other factors.
A)means
B)test statistic
C)degrees of freedom
D)variation

Accepted Answer

Matching observation pairs reduces the variation attributable to individual differences between the observations. This leads to a more accurate comparison of the means between the two related populations.

Question 10

When comparing two independent population means by using small samples selected from two independent normally distributed populations with equal variances,the correct test statistic to use is ____. A)Z B)t C)F D)t²

Accepted Answer

When comparing two independent population means with small sample sizes, the correct test statistic to use is the t-test. The t-test takes into account the sample sizes and the sample standard deviations to determine the significance of the difference between the means. The Z-test is used when the population standard deviation is known, which is not the case in this scenario. The F-test is used for comparing variances of two populations, which is not the case here either. The option D is not a recognized test statistic.

Question 11

In comparing the difference between two independent population means,by using two small independent samples,the sampling distributions of the population means are at least approximately ________________.
A)skewed right
B)skewed left
C)normal
D)binomial

Accepted Answer

According to the Central Limit Theorem, when the sample size is large enough (usually a sample size greater than 30), the sampling distribution of the mean tends to be normal, regardless of the shape of the original population distribution. In the case of small independent samples, if the populations are approximately normal or the sample sizes are not too small (e.g., greater than 10), then the sampling distributions of the means can also be considered normal.

Question 12

Given two independent normal distributions with s₁²- s₁² = 100,µ₁= µ₂ = 50,n₁= n₂ = 50,the sampling distribution of the mean difference ₁- ₂ will have a mean of _________. A)1 B)0 C)50 D)100

Accepted Answer

Since the two normal distributions are independent, their mean difference will also follow a normal distribution with mean = µ1-µ2 and standard deviation = sqrt((s1^2/n1) + (s2^2/n2)). Therefore, the mean of the sampling distribution of the mean difference will be µ1-µ2, which is 50-50=0. Therefore, the answer is choice B.

Question 13

Given the following information about a hypothesis test of the difference between two variances based on independent random samples,what is the calculated value of the test statistic? Assume that the samples are obtained from normally distributed populations. H_A: $\sigma$²_A> $\sigma$²_B, ₁ = 12, ₂ = 9,s₁ = 5,s₂ = 3,n₁ = 13,n₂ = 10. A)F = 2.0 B)F = 3.0 C)F = 1.667 D)F = 1.778 E)F = 2.778

Accepted Answer

The answer of Given the following information about a hypothesis...

Question 14

When comparing two independent population means where the population variances are known and n₁ and n₂ are sufficiently large,the correct test statistic to use is ____. A)Z B)t C)F D)t²

Accepted Answer

When comparing two independent population means and the population variances are known, the correct test statistic to use is the Z-score. This is because the sample size is sufficiently large, which allows us to make inferences about the population means using the standard normal distribution. The t-test would be used if the population variances were unknown or if the sample size was smaller. The F-test is used for comparing variances, not means. The fourth option, tP12S1S1P0, is not a valid test statistic.

Question 15

In testing the difference between the means of two normally distributed populations,if µ₁ = µ₂ = 50,n₁= 9,n₂ = 13,the degrees of freedom for the t statistic is ___________. A)22 B)21 C)19 D)20

Accepted Answer

The answer of In testing the difference between the means...

Question 16

When testing the difference for the population of paired differences in which two different observations are taken on the same units,the correct test statistic to use is ____. A)Z B)t C)F D)t²

Accepted Answer

When testing the difference for the population of paired differences, we compare the mean of the differences to a hypothesized value. Since the population variance of the differences is typically unknown, we use the t-test instead of the z-test. The t-test is used for small sample size and tests the null hypothesis that the mean difference is zero.

Question 17

In testing the difference between the means of two independent populations,the variances of the two samples can be pooled if the population variances are assumed to be ____________.
A)Unequal
B)Greater than the mean
C)Sum to 1
D)Equal

Accepted Answer

The variances of the two populations can only be pooled if they are assumed to be equal. If they are unequal, we cannot make assumptions about the common variance, and therefore cannot pool the variances.

Question 18

In testing the difference between two independent population means if the variances of the two populations are not equal the critical value of the t statistic is obtained by calculating ___________________. A)degrees of freedom B)the sum of the two sample sizes (n₁ + n₂) C)p-value D)pooled variance

Accepted Answer

When the variances of two populations are not equal, the degrees of freedom for the t-test are calculated using a specific formula (Welch's t-test) to adjust for the unequal variances.

Question 19

In order to test the effectiveness of a drug called XZR designed to reduce cholesterol levels,9 heart patients' cholesterol levels are measured before they are given the drug.The same 9 patients use XZR for two continuous months.After two months of continuous use,the 9 patients' cholesterol levels are measured again.The comparison of cholesterol levels before vs.after the administration of the drug is an example of testing the difference between two ____________
A)samples of equal variances
B)independent samples
C)paired samples
D)samples of unequal variances

Accepted Answer

The comparison of cholesterol levels before and after the administration of the drug involves measuring the same variable twice on the same individuals. Therefore, this is an example of paired samples where the two sets of measurements are dependent on each other. Options A, B, and D are not suitable because they involve different types of sample comparisons. Option A (equal variances) and option D (unequal variances) both refer to the assumption about the variances in the populations being compared, which is not relevant in this case. Option B (independent samples) involves comparing two different groups of individuals, which is not the case here.

Question 20

When testing the difference between two population proportions,__________ test statistic is used. A)Z B)t C)F D)t²

Accepted Answer

The appropriate test statistic for testing the difference between two population proportions is the Z-test statistic.

Quiz 10: Statistical Inferences Based on Two Samples

If we are testing the hypothesis about the mean of a population of paired differences with samples of n₁ = 10,n₂ = 10,the degrees of freedom for the t statistic is ____.

In general,the shape of the F distribution is _________.

In testing the difference between two independent population means,it is assumed that the level of measurement is at least ______________.

An experiment in which two different measurements are taken on the same units and inferences are made using the differences between the pairs of measurements is a(n) ______ experiment.

When comparing two independent population means when population variances are not known and the samples are normally distributed,the correct test statistic to use is ____.

When comparing two independent population variances,the correct test statistic to use is __________.

An experiment in which there is no relationship between the measurements on the different samples is a(n) ______ experiment.

The test of means for two related populations match the observations (matched pairs) in order to reduce the ________________ attributable to the difference between individual observations and other factors.

When comparing two independent population means by using small samples selected from two independent normally distributed populations with equal variances,the correct test statistic to use is ____.

In comparing the difference between two independent population means,by using two small independent samples,the sampling distributions of the population means are at least approximately ________________.

Given two independent normal distributions with s₁²- s₁² = 100,µ₁= µ₂ = 50,n₁= n₂ = 50,the sampling distribution of the mean difference ₁- ₂ will have a mean of _________.

When comparing two independent population means where the population variances are known and n₁ and n₂ are sufficiently large,the correct test statistic to use is ____.

In testing the difference between the means of two normally distributed populations,if µ₁ = µ₂ = 50,n₁= 9,n₂ = 13,the degrees of freedom for the t statistic is ___________.

When testing the difference for the population of paired differences in which two different observations are taken on the same units,the correct test statistic to use is ____.

In testing the difference between the means of two independent populations,the variances of the two samples can be pooled if the population variances are assumed to be ____________.

In testing the difference between two independent population means if the variances of the two populations are not equal the critical value of the t statistic is obtained by calculating ___________________.

When testing the difference between two population proportions,__________ test statistic is used.