Deck 9: Hypothesis Testing

Question 1

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

Answer 1

False

Question 2

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

Answer 2

False

Question 3

Testing H₀: µ $\ge$ 22 versus H_A: µ < 22,given $\alpha$ = .01,n = 100, = 21.431,and s = 1.295,we should not reject H₀.

Answer 3

False

Question 4

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

Question 5

Alpha ( $\alpha$ )is the probability that the test statistic would assume a value as or more extreme than the observed value of the test.

Question 6

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

Question 7

A Type I error is rejecting a true null hypothesis.

Question 8

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

Question 9

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

Question 10

Testing H₀: µ $\le$ 8 versus H_A: µ > 8,given $\alpha$ = .01,n = 25, = 8.112,and s = .16,we should reject the H₀.(Assume the sample is selected from a normally distributed population. )

Question 11

The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire.The population is normally distributed and the population standard deviation is known.She uses a Z test to test the null hypothesis that the mean tensile strength is 800 pounds per square inch.The calculated Z test statistic is a positive value that leads to a p-value of .045 for the test.If the significance level ( $\alpha$ )is .05,the null hypothesis would be rejected.

Question 12

When conducting a hypothesis test about a single mean,reducing the level of significance ( $\alpha$ )will increase the size of the rejection region.

Question 13

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

Question 14

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

Question 15

The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire.The population is normally distributed and the population standard deviation is known.She uses a Z test to test the null hypothesis that the mean tensile strength is less than or equal to 800 pounds per square inch.The calculated Z test statistic is a positive value that leads to a p-value of .067 for the test.If the significance level is .10,the null hypothesis would be rejected.

Question 16

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

Question 17

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

Question 18

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

Question 19

When conducting a hypothesis test about a single 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 20

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

Question 21

The rejection of a true null hypothesis is called a ______________ error.

A)Type I
B)Type II
C)Random
D) $\beta$

Question 22

Based on a random sample of 25 units of product X,the average weight is 102 lbs. ,and the sample standard deviation is 10 lbs.We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs.The alternative hypothesis can be written as H_A: µ > 100.(Assume the population is normally distributed. )

Question 23

Testing H₀: µ = 32 versus H_A: µ > 32 when = 36,s = 1.6,and n = 30 at $\alpha$ = .05,we should reject H₀.

Question 24

When we test H₀: µ $\le$ 3.0 versus H_A: µ > 3.0 when = 3.44,s = .57,and n = 13 at a significance level of .05,we fail to reject H₀.(Assume population normality)

Question 25

Testing H₀: µ $\le$ 42 versus H_A: µ > 42 when = 45,s = 1.2,and n = 15 at $\alpha$ = .01,we fail to reject the null hypothesis.(Assume that the population from which the sample is selected is normally distributed. )

Question 26

Based on a random sample of 25 units of product X,the average weight is 102 lbs. ,and the sample standard deviation is 10 lbs.We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs.Assume the population is normally distributed.The null hypothesis can be written: H₀: µ = 100.

Question 27

Testing H₀: µ $\ge$ 2.5 versus H_A: µ < 2.5 when = 2.46,s = .05,and n = 26 at $\alpha$ = .10 we reject the null hypothesis.(Assume that the population from which the sample is selected is normally distributed. )

Question 28

It can be established at = .05 that a majority of students favor the plus/minus grading system at a university if in a random sample of 500 students,270 favor the system.

Question 29

Based on a random sample of 25 units of product X,the average weight is 102 lbs. ,and the sample standard deviation is 10 lbs.We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs.Assume the population is normally distributed.At $\alpha$ = .01,we can reject the null hypothesis.

Question 30

A microwave manufacturing company has just switched to a new automated production system.Unfortunately,the new machinery has been frequently failing and requiring repairs and service.The company has been able to provide its customers with a completion time of 6 days or less.To analyze whether the completion time has increased,the production manager took a sample of 36 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days.At a significance level of .10,we can show that the completion time has increased.

Question 31

After testing at = .05 H₀: p = .33 versus H_A: p < .33 with = .20 and n = 100,we fail to reject H₀.

Question 32

Testing H₀: µ $\le$ .95 versus H_A: µ > .95 when = .99,s = .12,and n = 24 at alpha = .05,we reject H₀.(Assume a normally distributed population. )

Question 33

When we test H₀: p = .2 versus H_A: p $\neq$ .2 with = .26 and n = 100 at $\alpha$ = .05 we reject the null hypothesis.

Question 34

A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.At $\alpha$ = .10,we would fail to reject H₀.

Question 35

When testing a hypothesis about a single mean,if the sample size is 20,and the population standard deviation is unknown,the correct test statistic to use is ___________.

A) $\chi$
B)Z
C)t
D)p-value

Question 36

Testing H₀: p $\ge$ .7 versus H_A: p < .7 with = .63 and n = 100 at = .01,we fail to reject the null hypothesis.

Question 37

A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.At $\alpha$ = .05,we would reject the null hypothesis.

Question 38

Based on a random sample of 25 units of product X,the average weight is 102 lbs. ,and the sample standard deviation is 10 lbs.We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs.Assume the population is normally distributed.At $\alpha$ = .05,we fail to reject H₀.

Question 39

The sample evidence indicates that the average time an employee stays with a company in their current positions is less than 3 years at $\alpha$ = .01.A random sample of 50 employees yielded a mean of 2.79 years and s = .76.

Question 40

When testing a hypothesis about a single mean,if the sample size is 51,and the population standard deviation is known,the correct test statistic to use is ___________.

A) $\chi$
B)Z
C)t
D)p-value

Question 41

The _____ hypothesis is not rejected unless there is sufficient sample evidence to do so.

A)Research
B)Alternative
C)Null
D)Chi-square

Question 42

A null hypothesis is not rejected at given level of significance.As the assumed value of the mean gets further away from the true population mean,the type II error will _____________.

A)Increase
B)Decrease
C)Stay the same
D)Randomly fluctuate

Question 43

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

A)Z-test
B)Alternative
C)Null
D)Chi-square

Question 44

Determine the p-value for H₀: p $\le$ .5 versus H_A: p > .5 when n = 225 and = .54.

A).1131
B).2262
C).0082
D).8869

Question 45

Determine the p-value for H₀: p = .5 versus H_A: p $\neq$ .5 when n = 225 and = .54.

A).1131
B).2262
C).0164
D).0082

Question 46

Based on a random sample of 25 units of product X,the average weight is 102 lbs. ,and the sample standard deviation is 10 lbs.We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs.Assume the population is normally distributed.What is the critical value (given in terms of the value of the test statistic)at $\alpha$ = .05?

A)1.645
B)1.711
C)1.708
D)2.064

Question 47

As the type II error $\beta$ of statistical test increases,the power of the test _____________.

A)Increases
B)Decreases
C)Stays the same
D)Randomly fluctuates

Question 48

In testing H₀: µ $\le$ 23 versus H_A: µ > 23 when = 26,s = 6,and n = 30,what is the value of the z-statistic?

A)-2.74
B)15.00
C)1.09
D)2.74

Question 49

The value of the test statistic is compared with a(n)_______________ in order to decide whether the null hypothesis can be rejected.

A) $\alpha$
B) $\beta$
C)p-value
D)critical value

Question 50

In testing H₀: p = .2 versus H_A: p $\neq$ .2 with = .26 and n = 100,what is the value of the z-statistic?

A)1.50
B)1.33
C)-1.50
D)-1.33

Question 51

In testing H₀: µ = 23 versus H_A: µ > 23 when =26,s = 6,and n = 20,what is the value of the t-statistic?

A)10.00
B)2.24
C)-2.24
D)1.34

Question 52

For a fixed sample size,the lower we set $\alpha$ ,the higher is the ___________.

A)Type I error
B)Type II error
C)Random error
D)p-value

Question 53

__________is the probability of not rejecting H₀when H₀ is false.

A)Type I error
B)Type II error
C)Random error
D) $\alpha$

Question 54

In testing H₀: p $\ge$ .33 versus H_A: p < .33 with = .20 and n = 100,what is the value of the z-statistic?

A)2.77
B)-3.25
C)3.25
D)-2.77

Question 55

Determine the p-value for H₀: µ = 95 versus H_A: µ $\neq$ 95 when = 90.2,s = 9.92,and n = 37.

A).0032
B).0016
C).9968
D)less than .0001

Question 56

Assuming that the null hypothesis is true,the ______________ is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data.

A) $\alpha$
B) $\beta$
C)p-value
D)Type I error

Question 57

A(n)_________ hypothesis is the statement that is being tested.It usually represents the status quo and it is not rejected unless if there is convincing sample evidence that it is false.

A)Research
B)Alternative
C)Null
D)Chi-square

Question 58

When testing a hypothesis about a single mean,sample size of 200 is selected from a normally distributed population.If the population standard deviation is known,the correct test statistic to use is ___________.

A) $\chi$
B)Z
C)t
D)p-value

Question 59

Determine the p-value for H₀: µ $\ge$ 95 versus H_A: µ < 95 when = 90.2,s = 9.92,and n = 37.

A).9984
B).0032
C).0016
D)less than .0001

Question 60

Assuming a fixed sample size,as $\alpha$ (Type I error)decreases, $\beta$ (Type II error)___________.

A)Increases
B)Decreases
C)Stays the same
D)Randomly fluctuates

Question 61

Type II error is defined as the probability of ________________ H₀,when it should ___________.

A)failing to reject;be rejected
B)failing to reject;not be rejected
C)rejecting,not be rejected
D)rejecting,rejected

Question 62

A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.What is the critical value (given in terms of the value of the test statistic)at $\alpha$ = .10?

A)1.282
B)1.645
C)1.960
D)2.326

Question 63

For a given hypothesis test,if we do not reject H₀,and H₀ is true.

A)No error has been committed.
B)Type I error has been committed.
C)Type II error has been committed.
D)Type III error has been committed.

Question 64

If a two-sided null hypothesis cannot be rejected for a single mean at a given significance level,then the corresponding one-sided null hypothesis (i.e. ,the same sample size,the same standard deviation,and the same mean)will _________ be rejected at the same significance level.

A)Always
B)Sometimes
C)Never

Question 65

A null hypothesis H₀: µ $\ge$ 2.4 is not rejected at a significance level of 0.04.( $\alpha$ = 0.04).The standard deviation for the normally distributed population is known to be 0.40.Determine the Type II error,if we assume that the actual mean is 2.125 based on a sample size of 16.

A)8413
B)1587
C)3413
D)3177

Question 66

A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.What is the p-value for this test?

A)0511
B)1022
C)0548
D)0446

Question 67

If a two-sided null hypothesis is rejected for a single mean at a given significance level,the corresponding one- sided null hypothesis (i.e. ,the same sample size,the same standard deviation,and the same mean)will _________ be rejected at the same significance level.

A)Always
B)Sometimes
C)Never

Question 68

When testing a null hypothesis about a single population mean and the population standard deviation is unknown,if the sample size is less than 30,one compares the computed test statistic for significance with a value from the ___________ distribution.

A)t
B)Z
C)Binomial
D)Chi-square

Question 69

If a one-sided null hypothesis is rejected at a given significance level,then the corresponding two-sided null hypothesis (i.e. ,the same sample size,the same standard deviation,and the same mean)will _________ be rejected at the same significance level.

A)Always
B)Sometimes
C)Never

Question 70

Based on a random sample of 25 units of product X,the average weight is 102 lbs. ,and the sample standard deviation is 10 lbs.We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs.Assume the population is normally distributed.What is the sample value of the test statistic?

A)-1.00
B)3.16
C)1.00
D)2.00

Question 71

A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.What is the sample value of the test statistic?

A)1.348
B)1.661
C)3.452
D)1.635

Question 72

If a null hypothesis is rejected at a significance level of .05,it will ______ be rejected at a significance level of .01.

A)Always
B)Sometimes
C)Never

Question 73

Based on a random sample of 25 units of product X,the average weight is 102 lbs. ,and the sample standard deviation is 10 lbs.We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs.Assume the population is normally distributed.What is the critical value (given in terms of the value of the test statistic)at $\alpha$ = .01?

A)2.485
B)2.326
C)2.797
D)2.492

Question 74

A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.What is the critical value (given in terms of the value of the test statistic)at $\alpha$ = .01?

A)1.282
B)1.645
C)1.960
D)2.326

Question 75

A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.Which of the following does not represent a null hypothesis?

A)p < .66
B)p > .66
C)p = .66
D)p $\le$ .66

Question 76

A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.The alternative hypothesis is:

A)p < .66
B)p > .66
C)p = .66
D)p $\le$ .66

Question 77

Based on a random sample of 25 units of product X,the average weight is 102 lbs. ,and the sample standard deviation is 10 lbs.We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs.Assume the population is normally distributed.What is the p-value for this test?

A)8413
B)0228
C)3174
D)1587

Question 78

If a null hypothesis is rejected at a significance level of .01,it will ______ be rejected at a significance level of .05.

A)Always
B)Sometimes
C)Never

Question 79

If a one-sided null hypothesis for a single mean cannot be rejected at a given significance level,then the corresponding two-sided null hypothesis (i.e. ,the same sample size,the same standard deviation,and the same mean)will _________ be rejected at the same significance level.

A)Always
B)Sometimes
C)Never

Question 80

If a null hypothesis is not rejected at a significance level of .05,it will ______ be rejected at a significance level of .01.

A)Always
B)Sometimes
C)Never