Deck 10: Statistical Inferences Based on Two Samples

Question 1

Assume that we are constructing confidence interval for the difference in the means of two populations based on independent random samples.If both sample sizes and the distribution of both populations are highly skewed,then a confidence interval for the difference in the means can be constructed using the t test statistic.

Answer 1

False

Question 2

If the limits of the confidence interval of the difference between the means of two normally distributed populations were 8.5 and 11.5 at the 95% confidence level,then we can conclude that we are 95% certain that there is a significant difference between the two population means.

Answer 2

True

Question 3

When comparing two population means based on independent random samples,the pooled estimate of the variance is used if both population standard deviations are known.

Answer 3

False

Question 4

An independent samples experiment is an experiment in which there is no relationship between the measurements in the different samples.

Question 5

In testing the equality of population variances,two assumptions are required: independent samples and normally distributed populations.

Question 6

When comparing the variances of two normally distributed populations using independent random samples,if ,the calculated value of F will always be equal to one.

Question 7

In testing the difference between the means of two normally distributed populations using large independent random samples,the sample sizes from the two populations must be equal in order to use a Z statistic.

Question 8

In testing the difference between the means of two normally distributed populations using large independent random samples,the alternative hypothesis indicates no differences between the two specified means.

Question 9

In testing the difference between the means of two normally distributed populations using large independent random samples,we can only use a two-sided test.

Question 10

When we are testing a hypothesis about the difference in two population proportions based on large independent samples,we compute a combined (pooled)proportion from the two samples if we assume that there is no difference between the two proportions in our null hypothesis.

Question 11

If the limits of the confidence interval of the difference between the means of two normally distributed populations were from -2.6 and 1.4 at the 95% confidence level,then we can conclude that we are 95% certain that there is a significant difference between the two population means.

Question 12

In testing the difference between two means from two independent populations,the sample sizes do not have to be equal to be able to use the Z statistic.

Question 13

When testing the difference between two proportions selected from populations with large independent samples,the Z test statistic is used.

Question 14

When comparing two independent population means,if n₁ = 13 and n₂ = 10,degrees of freedom for the t statistic is 22.

Question 15

In testing the difference between two population variances,it is a common practice to compute the F statistic so that its value is always greater than or equal to one.

Question 16

In forming a confidence interval for ,only two assumptions are required: independent samples and sample sizes of at least 30.

Question 17

In an experiment involving matched pairs,a sample of 12 pairs of observations is collected.The degree of freedom for the t statistic is 10.

Question 18

In testing for the equality of variances from two independent populations,if the null hypothesis is false,the test could result in:

A)A Type I error.
B)Either a Type I error or a Type II error.
C)Neither a Type I error or a Type II error.
D)A Type II error.
E)Both a Type I error and a Type II error.

Question 19

The F statistic can assume either a positive or a negative value.

Question 20

In testing the difference between the means of two independent populations,if neither population is normally distributed,then the sampling distribution of the difference in means will be approximately normal provided that the sum of the sample sizes obtained from the two populations are at least 30.

Question 21

A financial analyst working for a financial consulting company wishes to find evidence that the average price-to-earnings ratio in the consumer industry is higher than average price-to-earnings ratio in banking industry.The alternative hypothesis is:

A) $\mu$ _consumer= $\mu$ _banking
B) $\mu$ _consumer $\le$ $\mu$ _banking
C) $\mu$ _consumer > $\mu$ _banking
D) $\mu$ _consumer< $\mu$ _banking
E) $\mu$ _consumer $\neq$ 0 $\mu$ _banking

Question 22

Given the following information about a hypothesis test of the difference between two means based on independent random samples,what is the standard deviation of the difference between the two means? Assume that the samples are obtained from normally distributed populations having equal variances. H_A: µ_A> µ_B, ₁ = 12, ₂ = 9,s₁ = 5,s₂ = 3,n₁ = 13,n₂ = 10.

A)1.792
B)1.679
C)2.823
D)3.210
E)1.478

Question 23

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 administering the drug is an example of testing the difference between:

A)Two means from independent populations.
B)Two population variances from independent populations.
C)Two population proportions.
D)Matched pairs from two dependent populations.

Question 24

A new company is in the process of evaluating its customer service.The company offers two types of sales: 1.Internet sales;2.Store sales.The marketing research manager believes that the Internet sales are more than 10% higher than store sales.The alternative hypothesis for this problem would be stated as:

A)P_internet- P_store> 0
B)P_internet- P_store< 0
C)P_internet- P_store $\ge$ 0
D)P_internet- P_store $\le$ .10
E)P_internet- P_store > .10

Question 25

In testing the difference between two means from two normally distributed independent populations,the distribution of the difference in sample means will be:

A)Normally distributed only if sample sizes are equal.
B)Normally distributed only if both population standard deviations are known.
C)Normally distributed.
D)Normally distributed if both sample sizes are very large.
E)Normally distributed only if both population variances are equal.

Question 26

A new company is in the process of evaluating its customer service.The company offers two types of sales: 1.Internet sales;2.Store sales.The marketing research manager believes that the Internet sales are more than 10% higher than store sales.The null hypothesis would be:

A)P_internet- P_store> .10
B)P_internet- P_store< .10
C)P_internet- P_store $\ge$ .10
D)P_internet- P_store $\le$ .10
E)P_internet- P_store = .10

Question 27

In testing the difference between the means of two normally distributed populations using large,independent random samples with known variances,the correct test statistic to use is:

A)Z statistic
B)t statistic
C)F statistic
D)Chi-square statistic
E)None of the above

Question 28

If the Z statistic (critical value)is incorrectly used in lieu of the t statistic when comparing two means from independent populations using small samples,the chance of rejecting the null hypothesis __________.

A)Increases
B)Decreases
C)Remains the same

Question 29

When testing the difference between two population proportions using large independent random samples,__________ test statistic is used.

A)Z
B)t
C)F
D)Chi-square
E)None of the above

Question 30

In testing the difference between the means of two normally distributed populations using small independent random samples,the most appropriate test statistic is the _________ statistic.

A)Z
B)t
C)F
D)Chi-square
E)None of the above

Question 31

Given the following information about a hypothesis test of the difference between two means based on independent random samples,what is the calculated value of the test statistic? Assume that the samples are obtained from normally distributed populations having equal variances. H_A: µ_A> µ_B, ₁ = 12, ₂ = 9,s₁ = 5,s₂ = 3,n₁ = 13,n₂ = 10.

A)t = 1.96
B)t = 1.5
C)t = 2.823
D)t = 1.674
E)t = 1.063

Question 32

In testing for the equality of means from two independent populations,if the null hypothesis is rejected,the test could result in:

A)A Type I error.
B)Either a Type I error or a Type II error.
C)Neither a Type I error or a Type II error.
D)A Type II error.
E)Both a Type I error and a Type II error.

Question 33

In which of the following tests is the variable of interest the difference between the values of the observations from the two samples rather than the actual observations themselves?

A)A test of hypothesis about the mean of a population of paired differences selected from two related samples.
B)A test of hypothesis about the difference between the means of two normally distributed populations using large independent samples.
C)A test of hypothesis about the difference between the means of two normally distributed populations using small independent samples.
D)A test of hypothesis about the difference between two population proportions,using large independent random samples.
E)A test of hypothesis about the difference between the variances of two normally distributed populations using independent samples.

Question 34

In testing for the equality of means from two independent populations,if the hypothesis of equal population means is rejected at $\alpha$ = .01,it will __________ be rejected at $\alpha$ = .05.

A)Always
B)Sometimes
C)Never

Question 35

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)19
B)18
C)9
D)8
E)10

Question 36

Given the following information about a hypothesis test of the difference between two means based on independent random samples,which one of the following is the correct rejection region at a significance level of .05? H_A: µ_A> µ_B, ₁ = 12, ₂ = 9,s₁ = 4,s₂ = 2,n₁ = 13,n₂ = 10.

A)Reject H₀ if Z > 1.96
B)Reject H₀ if Z > 1.645
C)Reject H₀ if t > 1.721
D)Reject H₀ if t > 2.08
E)Reject H₀ if t > 1.782

Question 37

When comparing the variances of two normally distributed populations using independent random samples,the correct test statistic to use is __________.

A)Z
B)t
C)F
D)Chi-square
E)None of the above

Question 38

If the Z statistic (critical value)is incorrectly used in lieu of the t statistic when comparing two means from independent populations using small samples,the chance of committing a Type II error __________.

A)Increases
B)Decreases
C)Remains the same

Question 39

If we are testing the difference between the means of two normally distributed independent populations with samples of n₁ = 10,n₂ = 10,the degrees of freedom for the t statistic is ____.

A)19
B)18
C)9
D)8
E)20

Question 40

When testing a hypothesis about the mean of a 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)Chi-square
E)None of the above

Question 41

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

Question 42

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

A)skewed right
B)skewed left
C)normal
D)binomial

Question 43

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

Question 44

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

Question 45

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

Question 46

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

Question 47

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

A)Z
B)t
C)F
D)t²

Question 48

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

Question 49

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

Question 50

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

Question 51

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

Question 52

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

Question 53

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

Question 54

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

Question 55

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

Question 56

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

Question 57

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

Question 58

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

Question 59

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

Question 60

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

A)Z
B)t
C)F
D)t²

Question 61

Find a 95 percent confidence interval for µ₁- µ₂,where n₁= 50,n₂ = 75, ₁ = 82, ₂ = 76, $\sigma$ ₁² = 8 and $\sigma$ ₂² = 6.

A)(5.04 6.96)
B)(5.53 6.47)
C)(5.19 6.81)
D)(5.41 6.59)

Question 62

Find a 98 percent confidence interval for the paired difference. .

A)(-1.118 4.318)
B)(-1.277 4.477)
C)(1.075 2.125)
D)(1.104 2.096)

Question 63

In testing the equality of population variance,what assumption(s)should be considered?

A)Independent samples
B)Equal sample sizes
C)Normal distribution of the populations
D)A and B
E)A and C

Question 64

Find a 95 percent confidence interval for µ₁- µ₂,where n₁= 15,n₂ = 10, ₁ = 1.94, ₂ = 1.04,s₁² = .2025 and s₂² = .0676.(Assume equal population variances)

A)(0.587 1.213)
B)(0.848 0.952)
C)(0.629 1.171)
D)(0.573 1.227)

Question 65

When we test H₀: $\mu$ ₁ $\le$ $\mu$ ₂,H_A: $\mu$ ₁ > $\mu$ ₂at $\alpha$ = .10,where ₁ = 77.4, ₂ = 72.2,s₁ = 3.3,s₂ = 2.1,n₁ = 6,n₂= 6,what is the estimated pooled variance?

A)2.77
B)6.38
C)2.52
D)7.65

Question 66

Find a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2 where ₁ = .05, ₂ = .04,n₁= 500,n₂ = 2000.

A)(-0.0037 0.0237)
B)(-0.0076 0.0276)
C)(0.0004 0.0196)
D)(0.0098 0.0102)

Question 67

When testing H₀: $\sigma$ ₁² $\le$ $\sigma$ ₂² H_A: $\sigma$ ₁²> $\sigma$ ₂² where s₁² = .004,s₂² = .002,n₁ = 4,n₂ = 7 at $\alpha$ = .05,what is the decision on H₀?

A)Reject the null hypothesis
B)Do not reject the null hypothesis

Question 68

Parameters of the F distribution include:

A)n₁
B)degrees of freedom
C)n₂
D)A and C
E)None of the above

Question 69

Construct a 95 percent confidence interval for $\mu$ ₁- v₂,where ₁ = 34.36, ₂ = 26.45,s₁ = 9,s₂= 6,n₁ = 10,n₂ = 16.(Assume equal population variance)

A)(1.59 14.23)
B)(2.10 13.72)
C)(1.86 13.96)
D)(1.88 13.94)

Question 70

What is the value of the computed F-statistic for testing equality of population variances where s₁² = .004,s₂² = .002? Consider H_A: $\sigma$ ₁²> $\sigma$ ₂².

A)1
B)0.001
C)0.05
D)2

Question 71

With a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2 where ₁ = .05, ₂ = .04,n₁= 500,n₂ = 2000 of (-.0076 .0276)can we reject the null hypothesis at $\alpha$ = .10?

A)Yes,reject the null hypothesis
B)No;we can't reject the null hypothesis

Question 72

Find a 95 percent confidence interval for µ₁- µ₂,where n₁= 9,n₂ = 6, ₁ = 64, ₂ = 59,s₁² = 6 and s₂² = 3.(Assume equal population variances)

A)(2.357 7.643)
B)(2.494 7.506)
C)(2.528 7.472)
D)(3.840 6.160)

Question 73

When testing H₀: $\sigma$ ₁² $\le$ $\sigma$ ₂² H_A: $\sigma$ ₁²> $\sigma$ ₂² where s₁² = .004,s₂² = .002,n₁ = 4,n₂ = 7 at $\alpha$ = .05,what critical value do we use?

A)1.833
B)1.796
C)4.12
D)4.76

Question 74

When testing H₀: $\mu$ ₁ - $\mu$ ₂ = 2,H_A: $\mu$ ₁ - $\mu$ ₂ > 2,where ₁ = 522, ₂ = 516, $\sigma$ ₁² = 28, $\sigma$ ₂² = 24,n₁= 40,n₂ = 30,at $\alpha$ = .01,what is the test statistic?

A)4.91
B)2.33
C)3.27
D)2.67

Question 75

Find a 95 percent confidence interval for the difference between the proportions of older and younger drivers who have tickets where ₁ = .275, ₂ = .25,n₁= 1000,n₂ = 1000.

A)(-.007 .057)
B)(.024 .026)
C)(-.002 .052)
D)(-.014 .064)

Question 76

When we test H₀: p₁- p₂ $\le$ .01,H_A: p₁ - p₂ > .01 at $\alpha$ = .05 where ₁ = .08, ₂ = .035,n₁= 200,n₂ = 400,what is the standard deviation used in the calculation of the test statistic?

A)0.0005
B)0.3277
C)0.0213
D)0.0134

Question 77

Find a 95 percent confidence interval for the difference between means where n₁ = 50,n₂= 36, ₁ = 80, ₂ = 75, $\sigma$ ₁² = 5 and $\sigma$ ₂² = 3.

A)(4.16 5.84)
B)(3.30 6.70)
C)(4.40 5.60)
D)(4.64 5.36)

Question 78

When testing H₀: $\sigma$ ₁²= $\sigma$ ₁²,H_A: $\sigma$ ₁²> $\sigma$ ₂² at $\alpha$ = .01 where n₁ = 5,n₂= 6,s₁² = 15750,s₂² = 10920 what critical value do we use?

A)2.821
B)11.39
C)8.75
D)1.443

Question 79

What is the value of the F-statistic for H₀: $\sigma$ ₁² $\le$ $\sigma$ ₁²,H_A: $\sigma$ ₁²> $\sigma$ ₁²,where s₁= 3.3,and s₂ = 2.1.

A)2.47
B)1.57
C)6.48
D)6.10

Question 80

When testing H₀: $\mu$ ₁ - $\mu$ ₂ = 2,H_A: $\mu$ ₁ - $\mu$ ₂> 2,where ₁ = 522, ₂ = 516, $\sigma$ ₁² = 28, $\sigma$ ₂² = 24,n₁= 40,n₂ = 30,at $\alpha$ = .01,what can we conclude?

A)Fail to reject H₀
B)Reject H₀