Deck 7: Confidence Intervals

Question 1

If the significance level is .10,the null hypothesis would be rejected.

Answer 1

True

Question 2

When conducting a hypothesis test about a population mean,reducing the level of significance will increase the size of the rejection region.

Answer 2

False

Question 3

The level of significance indicates the probability of rejecting a false null hypothesis.

Answer 3

False

Question 4

If the significance level is .01,the null hypothesis would be rejected.

Question 5

In hypothesis testing,a test statistic is computed from sample data and is used in making a decision about whether or not to reject the null hypothesis.

Question 6

A Type II error is failing to reject a false null hypothesis.

Question 7

The significance level, $\alpha$ ,is the probability that the test statistic would assume a value as or more extreme than the observed value of the test statistic.

Question 8

As the level of significance increases,we are more likely to reject the null hypothesis.

Question 9

You cannot make a Type II error when the null hypothesis is true.

Question 10

Everything else being constant,increasing the sample size decreases the probability of committing a Type II error.

Question 11

The null hypothesis is a statement that will be accepted only if there is convincing sample evidence that it is true.

Question 12

If the significance level is .05,the null hypothesis would be rejected.

Question 13

For a hypothesis test about a population mean,if the level of significance is less than the p-value,the null hypothesis is rejected.

Question 14

The power of a statistical test is the probability of rejecting the null hypothesis when it is true.

Question 15

The larger the p-value,the more we doubt the null hypothesis.

Question 16

When conducting a hypothesis test about a population mean,other relevant factors held constant,increasing the level of significance from .05 to .10 will reduce the probability of a Type I error.

Question 17

When conducting a hypothesis test about a population mean,other relevant factors held constant,increasing the level of significance from .05 to .10 will reduce the probability of a Type II error.

Question 18

The further the hypothesized mean is from the actual mean,the greater the power of the test.

Question 19

A Type I error is rejecting a true null hypothesis.

Question 20

If the significance level is .05,the null hypothesis would be rejected.

Question 21

Which statement is incorrect?

A)The null hypothesis contains the equality sign.
B)When a false null hypothesis is not rejected,a Type II error has occurred.
C)We reject the null hypothesis whenever the p-value is less than the significance level.
D)Rejecting the null hypothesis when it should not be rejected is a Type I error.
E)If we fail to reject the null hypothesis,then it is proven that null hypothesis is true.

Question 22

When testing for a difference between two population proportions based on large,independent samples,the test statistic used is based on the z distribution.

Question 23

A Type II error occurs if we _________ H₀ when it should ___________.

A)fail to reject;be rejected
B)fail to reject;not be rejected
C)reject,not be rejected
D)reject,rejected
E)reject,accepted

Question 24

If a null hypothesis is NOT rejected at a significance level of 0.05,it will ______ be rejected at a significance level of _____.

A)always,0.10
B)sometimes,0.01
C)never,0.01
D)never,0.10
E)always,0.01

Question 25

If a one-sided hypothesis test for a population mean yields a p-value of 0.041,then what is the smallest level of significance at which the null hypothesis in the corresponding two-sided hypothesis test can be rejected?

A)10%
B)5%
C)2.5%
D)1%
E)0.1%

Question 26

If the null hypothesis in a one-sided hypothesis test for a population mean is rejected at the 5% level of significance,then the null hypothesis in the corresponding hypothesis two-sided test is guaranteed to be rejected at the ____ level of significance.

A)10%
B)5%
C)2.5%
D)1%
E)0.1%

Question 27

In testing the difference between the means of two normally distributed populations with known population standard deviations,the alternative hypothesis indicates no differences between the two specified means.

Question 28

In testing the difference between the means of two normally distributed populations with known population standard deviations,we can only use a two-sided test.

Question 29

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 30

When the null hypothesis is not rejected,there is no possibility of making a Type I error.

Question 31

When testing a hypothesis about a population proportion,if np₀ $\geq$ 5 and n(1 - p₀) $\geq$ 5,then the test statistics is based on the ___ distribution.

A)z
B)t
C)F
D)chi-square
E)exponential

Question 32

In testing the difference between the means of two normally distributed populations with known population standard deviations,the two sample sizes must be equal.

Question 33

If the null hypothesis in a two-sided hypothesis test for a population mean cannot be rejected at the 10% level of significance,then it is still possible that the null hypothesis in the corresponding one-sided hypothesis test could be rejected at the ____ level of significance.

A)10%
B)5%
C)2.5%
D)1%
E)0.1%

Question 34

If a one-sided hypothesis test for a population mean yields a p-value of 0.023,then what is the smallest level of significance at which the null hypothesis in the corresponding two-sided hypothesis test can be rejected?

A)10%
B)5%
C)2.5%
D)1%
E)0.1%

Question 35

For a given hypothesis test,if we do not reject H₀ when H₀ is true then which one of the following statements is true?

A)No error has been committed.
B)Type I error has been committed.
C)Type II error has been committed.
D)The power of the test has increased.
E)The power of the test has decreased.

Question 36

Consider testing the difference between the means of two populations with known population standard deviations.If neither population is normally distributed,then the sampling distribution of the difference in sample means will still be approximately normal provided that the sample sizes are sufficiently large and the samples are independent.

Question 37

In testing the difference between the means of two normally distributed populations with known population standard deviations,the samples we take from each population must be independent.

Question 38

If a null hypothesis is rejected at a significance level of 0.01,it will ______ be rejected at a significance level of _____.

A)always,0.05
B)never,0.05
C)always,0.01
D)never,0.01
E)never,0.10

Question 39

If a null hypothesis is rejected at a significance level of 0.05,it will ______ be rejected at a significance level of _____.

A)always,0.01
B)sometimes,0.01
C)never,0.01
D)never,0.10
E)sometimes,0.10

Question 40

When the null hypothesis is true,there is no possibility of making a Type I error.

Question 41

The smaller the _____,the stronger the evidence is against the null hypothesis.

A)Type II error
B)Type I error
C)rejection point
D)p-value
E)sample size

Question 42

A decision in a hypothesis test can be made by using _____.

A)a p-value.
B)a critical value.
C)the sample size.
D)either a p-value or a critical value.
E)either a critical value or the sample size.

Question 43

In a two-sided hypothesis test,if the p-value is less than $\alpha$ ,then

A)H₀ is rejected.
B)H₀ is not rejected.
C)H₀ may or may not be rejected depending on the sample size n.
D)additional information is needed to make a decision about H₀.
E)H_a is rejected

Question 44

The power of a statistical test is the probability of ______________ the null hypothesis when it is ________.

A)not rejecting,false
B)not rejecting,true
C)rejecting,false
D)rejecting,true
E)accepting,false

Question 45

For the following hypothesis test where H₀: ? ? 10 vs.H_a: ? > 10,we reject H₀ at level of significance $\alpha$
And conclude that the true mean is greater than 10 when the true mean is really 8.Based on this information we can state that we have:

A)Made a Type I error
B)Made a Type II error
C)Made a correct decision
D)Increased the power of the test
E)Decreased the power of the test

Question 46

What is the value of the calculated test statistic?

A)z = 6.416
B)z = 3.208
C)z = -3.208
D)z = -6.416
E)z = 1.833

Question 47

When carrying out a test of H₀: p = .4 versus H_a: p < .4 and z is the calculated test statistic,we reject H₀ at level of significance $\alpha$ When:

A)z < - $z _ { \alpha / 2 }$
B)z < - $z _ { \alpha }$
C)z > $z _ { \alpha }$
D)p-value > $\alpha$
E)p-value > 2 $\alpha$

Question 48

The null and alternative hypotheses to test whether the mean lifetime of the new cartridges exceeds that of the old cartridges is _____.

A)H_O: μ = 1502.5 vs.H_A: μ ≠ 1502.5
B)H_O: μ ≥ 1511.4 vs.H_A: μ < 1511.4
C)H_O: μ ≥ 1502.5 vs.H_A: μ < 1502.5
D)H_O: μ ≠ 1502.5 vs.H_A: μ = 1502.5
E)H_O: μ ≤ 1502.5 vs.H_A: μ > 1502.5

Question 49

When conducting a hypothesis test about a population mean at a given level of significance,as the sample size n increases the power of the test _____.

A)decreases
B)increases
C)may increase or decrease
D)remains the same
E)will converge to the probability of a Type II error.

Question 50

When carrying out a test of H₀: ? = 10 vs.H_a: ? ? 10 by using a p-value,we reject H₀ at level of significance alpha when the p-value is:

A)Greater than $\alpha$ /2
B)Greater than $\alpha$
C)Less than $\alpha$
D)Less than $\alpha$ /2
E)Less than $z _ { \alpha }$

Question 51

For the following hypothesis test where H₀: ? ? 10 vs.H_a: ? > 10,we reject H₀ at level of significance $\alpha$ And conclude that the true mean is greater than 10 when the true mean is really 14.Based on this information we can state that we have:

A)Made a Type I error
B)Made a Type II error
C)Made a correct decision
D)Increased the power of the test
E)Decreased the power of the test

Question 52

A researcher suspects that the unemployment rate in her province is greater than 8%.What is the appropriate alternative hypothesis?

A)H_a: p ≤ 0.08
B)H_a: p = 0.08
C)H_a: p ≥ 0.08
D)H_a: p < 0.08
E)H_a: p > 0.08

Question 53

When conducting a hypothesis test about a population mean at a given level of significance,as the sample size n increases the probability of a Type II error:

A)decreases.
B)increases.
C)may increase or decrease.
D)remains the same.
E)will converge to the probability of a Type I error.

Question 54

What is the correct statement of null and alternative hypothesis?

A)H₀: p < .18 and H_A: p ≥ .18
B)H₀: p ≤ .18 and H_A: p > .18
C)H₀: p = .18 and H_A: p ≥ .18
D)H₀: p > .18 and H_A: p ≤ .18
E)H₀: p ≤ .20 and H_A: p > .20

Question 55

The appropriate test statistic to test the hypotheses is _____.

A)56.09
B)3.74
C)22.34
D)-3.74
E)-22.34

Question 56

Suppose that you are conducting a hypothesis test about a population mean.Holding all other relevant factors constant,which of the following actions will result in an increase in the size of the rejection region?

A)Increase the sample size.
B)Decrease the sample size.
C)Increase the sample size and decrease the level of significance.
D)Decrease the sample size and increase the level of significance.
E)Increase the level of significance.

Question 57

When carrying out a test of H₀: ? = 10 vs.H_a: ? > 10 by using a critical value,we reject H₀ at level of significance $\alpha$ When the calculated test statistic is:

A)Less than $z _ { \alpha }$
B)Less than - $z _ { \alpha }$
C)Greater than $z _ { \alpha / 2 }$
D)Greater than $Z _ { \alpha }$
E)Less than the p-value

Question 58

A professional basketball player is averaging 21 points per game.He will be retiring at the end of this season.The team has multiple options to replace him.However,the owner feels that signing a replacement is only justified,if he can average more than 22 points per game.Which of the following are the appropriate hypotheses for this problem?

A)H₀: μ ≤ 21 vs.H_a: μ > 21
B)H₀: μ ≤ 22 vs.H_a: μ > 22
C)H₀: μ ≥ 21 vs.H_a: μ < 21
D)H₀: μ ≥ 22 vs.H_a: μ < 22
E)H₀: μ ≥ 22 vs.H_a: μ = 22

Question 59

If a two-sided hypothesis test for a population mean yields a p-value of 0.0651,then what is the smallest level of significance at which the null hypothesis in a corresponding one-sided hypothesis test can be rejected?

A)10%
B)5%
C)2.5%
D)1%
E)0.1%

Question 60

The average customer waiting time at a fast food restaurant has been 7.5 minutes.The customer waiting time has a normal distribution.The manager claims that the use of a new system will decrease average customer waiting time.What is the null and alternative hypothesis for this scenario?

A)H₀: μ = 7.5 and H_a ≠ 7.5
B)H₀: μ ≤ 7.5 and H_a > 7.5
C)H₀: μ ≥ 7.5 and H_a < 7.5
D)H₀: μ > 7.5 and H_a ≥ 7.5
E)H₀: μ > 7.5 and H_a ≤ 7.5

Question 61

What is the rejection point for α = .05 to test the hypotheses?

A)1.645
B)-1.645
C)1.96
D)1.28
E)-1.96

Question 62

The appropriate test statistic to test the hypotheses is _____.

A)2.47
B)34.13
C)478.16
D)-34.13
E)-2.47

Question 63

The test statistic is _____.

A)-16.00
B)-4.00
C)-2.00
D)2.00
E)4.00

Question 64

The p-value corresponding to the test statistic is _____.

A)0.0000
B)0.0068
C)-0.0068
D)0.0136
E)-0.0136

Question 65

How much evidence do we have that the new cartridge is better than the old?

A)No evidence
B)Some evidence
C)Strong evidence
D)Very strong evidence
E)Extremely strong evidence

Question 66

The test statistic is _____.

A)-2.83
B)-1.41
C)-2.00
D)2.83
E)1.41

Question 67

How much evidence do we have that the shipment is meeting the specified value?

A)No evidence
B)Some evidence
C)Strong evidence
D)Very Strong evidence
E)Extremely Strong evidence

Question 68

The null and alternative hypotheses to test whether the shipment meets the specified value is _____.

A)H₀: µ ≥ 350 H_a: µ < 350
B)H₀: µ ≠ 375 H_a: µ = 375
C)H₀: µ = 375 H_a: µ ≠ 375
D)H₀: µ ≥ 375 H_a: µ < 375
E)H₀: µ ≤ 375 H_a: µ > 375

Question 69

How much evidence do we have to reject the null hypothesis?

A)No evidence
B)Some evidence
C)Strong evidence
D)Very Strong evidence
E)Extremely Strong evidence

Question 70

The test statistic is _____.

A)4.50
B)47.61
C)9.00
D)-47.61
E)-4.50

Question 71

The p-value is _____.

A)0.0001
B)0.0002
C)0.0228
D)0.0456
E)-0.0228

Question 72

How much evidence do we have that the manufacturer's claim is false?

A)No evidence
B)Some evidence
C)Strong evidence
D)Very Strong evidence
E)Extremely Strong evidence

Question 73

The null and alternative hypotheses to determine is the figure has changed is _____.

A)H₀: µ = 74,914 H_a: µ ≠ 74,914
B)H₀: µ ≥ 74,914 H_a: µ < 74,914
C)H₀: µ ≤ 74,914 H_a: µ > 74,914
D)H₀: µ ≠ 74,914 H_a: µ = 74,914
E)H₀: µ ≤ 81,342 H_a: µ > 81,342

Question 74

The test statistic to test these hypotheses is _____.

A)-2.83
B)-6.32
C)5.64
D)-5.64
E)2.82

Question 75

The p-value is _____.

A).0024
B)-.0024
C).0000
D)-.0048
E).0046

Question 76

The null and alternative hypothesis to test if the average time to complete the test had changed from 120 minutes is _____.

A)H₀: µ = 120 H_a: µ ≠ 120
B)H₀: µ ≥ 120 H_a: µ < 120
C)H₀: µ ≤ 120 H_a: µ > 120
D)H₀: µ ≠ 120 H_a: µ = 120
E)H₀: µ ≥ 118 H_a: µ < 118

Question 77

The null and alternative hypotheses to test that the manufacturer's claim is false is _____.

A)H₀: µ ≤ .995 H_a: µ > .995
B)H₀: µ ≠ 1 H_a: µ = 1
C)H₀: µ ≥ 1 H_a: µ < 1
D)H₀: µ = 1 H_a: µ ≠ 1
E)H₀: µ ≤ 1 H_a: µ > 1

Question 78

How much evidence is there that the major engine failure will occur after 90,000 km?

A)No evidence
B)Some evidence
C)Strong evidence
D)Very strong evidence
E)Extremely strong evidence

Question 79

The p-value is _____.

A).0793
B).1586
C).0023
D).0046
E).0456

Question 80

The null and alternative hypotheses to test the claim that the mean distance traveled before a major engine failure is more than 90,000 km is _____.

A)H_O: μ = 90,000 vs.H_A: μ ≠ 90,000
B)H_O: μ ≥ 90,000 vs.H_A: μ < 90,000
C)H_O: μ ≥ 96,700 vs.H_A: μ < 96,700
D)H_O: μ ≠ 90,000 vs.H_A: μ = 90,000
E)H_O: μ ≤ 90,000 vs.H_A: μ > 90,000