Deck 9: Hypothesis Testing

Question 1

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

Answer 1

True

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

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

Answer 3

True

Question 4

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 (α)is .05,the null hypothesis would be rejected.

Question 5

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

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

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

Question 8

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

Question 9

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

Question 10

We are testing H₀: ? ? 8;versus H_A: ? > 8.Given ? = .01,n = 25, $\bar { X } = 8.112$
and s = .16,we should reject the H₀.(Assume the sample is selected from a normally distributed population. )

Question 11

A Type I error is rejecting a true null hypothesis.

Question 12

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

Question 13

Alpha (α)is the probability that the test statistic would assume a value at or more extreme than the observed value of the test.

Question 14

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

Question 15

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

Question 16

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

Question 17

We are testing H₀: ? ? 22;versus H_A: ? < 22.Given ? = .01,n = 100, $\bar { X } = 21.431$
and ? = 1.295,we should not reject H₀.

Question 18

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 19

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 20

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

Question 21

The HR department tested how long employees stays with the company in their current positions.A random sample of 50 employees yielded a mean of 2.79 years and σ = .76.The sample evidence indicates that the average time is less than 3 years and is significant at α = .01.

Question 22

After testing H₀: p = .33;versus H_A: p < .33;at ? = .05,with $\hat { p } = .20$
and n = 100,we do not reject H₀.

Question 23

We test H₀: ? ? 3.0;versus H_A: ? > 3.0.If $\bar { X } = 3.44$
s = .57,and n = 13,at a significance level of .05,we do not reject H₀.(Assume population normality. )

Question 24

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

Question 25

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 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 whether 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.One way of expressing the null hypothesis is H₀: μ = 100.

Question 27

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 α = .05,we do not reject H₀.

Question 28

We are testing H₀: µ ? 42;versus H_A: µ > 42.When $\bar { Y } = 45$
s = 1.2,and n = 15,at ? = .01 we do not reject the null hypothesis.(Assume that the population from which the sample is selected is normally distributed. )

Question 29

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 α = .05,we would reject the null hypothesis.

Question 30

A recent study conducted by the state government attempts to determine whether the voting public supports a 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 α = .10,we would not reject H₀.

Question 31

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

A)Type I
B)Type II
C)Random
D)β

Question 32

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)r
B)z
C)t
D)p-value

Question 33

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 34

We are testing H₀: ? = 32;versus H_A: ? > 32.If $\overline { \mathrm { X } } = 36$
s = 1.6,and n = 30 at ? = .05,we should reject H₀.

Question 35

When we test H₀: p = .2;versus H_A: p ?.2,with $\hat { p } = .26$
and n = 100,at alpha = .05,we reject the null hypothesis.

Question 36

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 α = .01,we can reject the null hypothesis.

Question 37

We are testing H₀: ? ? 2.5;versus H_A: ? < 2.5.When $\bar { X } = 2.46$
s = .05,and n = 26,at ? = .10 we reject the null hypothesis.(Assume that the population from which the sample is selected is normally distributed. )

Question 38

We are testing H₀: p ? .7;versus H_A: p < .7.With $\hat { p } = .63$
and n = 100,at ? = .01,we do not reject the null hypothesis.

Question 39

It can be established at α = .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 40

We are testing H₀: ? ? .95;versus H_A: ? > .95.When $\bar { X } = .99$
s = .12,and n = 24,at alpha = .05,we reject H₀.(Assume a normally distributed population. )

Question 41

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 42

For a fixed sample size,the lower we set α,the higher is the ___________.

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

Question 43

When testing a hypothesis about a single mean,a 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)r
B)z
C)t
D)p-value

Question 44

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

A)α
B)β
C)p-value
D)critical value

Question 45

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

Question 46

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

A)r
B)z
C)t
D)p-value

Question 47

As the Type II error β of statistical test increases,the power of the test _____________.

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

Question 48

A recent study conducted by the state government attempts to determine whether the voting public supports a 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 ≤ .66

Question 49

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 50

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

A)Research
B)Alternative
C)Null
D)True

Question 51

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)Hypergeometric

Question 52

Assuming a fixed sample size,as α (Type I error)decreases,β (Type II error)___________.

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

Question 53

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

A)z test
B)Alternative
C)Null
D)True

Question 54

____________ is the probability of not rejecting H₀ when H₀ is false.

A)Type I error
B)Type II error
C)Random error
D)α

Question 55

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)α
B)β
C)p-value
D)Type I error

Question 56

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 57

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

A)Research
B)Alternative
C)Null
D)True

Question 58

A null hypothesis is not rejected at a 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 59

A recent study conducted by the state government attempts to determine whether the voting public supports a 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.Identify the null hypothesis.

A)p ≠ .66
B)p > .66
C)p ≤ .66

Question 60

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

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

Question 61

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 62

A recent study conducted by the state government attempts to determine whether the voting public supports a 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 to test the claim at α = .01?

Question 63

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

Question 64

In testing H₀: μ ≤ 23;versus H_A: μ > 23,when
= 26,σ = 6,and n = 30,what is the value of the test statistic?

Question 65

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?

Question 66

A 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 67

Determine the p-value for H₀: μ ≥ 95;versus H_A: μ < 95,when

Question 68

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 69

In testing H₀: p = .2;versus H_A: p ≠ .2,with
= .26 and n = 100,what is the value of the test statistic?

Question 70

In testing H₀: p ≥ .33;versus H_A: p < .33,with
= .20 and n = 100,what is the value of the test statistic?

Question 71

Determine the p-value for H₀: p ≤ .5;versus H_A: p > .5,when n = 225 and

Question 72

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 used to test the claim at α = .05?

Question 73

Determine the p-value for H₀: p = .5;versus H_A: p ≠ .5,when n = 225 and V

Question 74

For the following hypothesis test,where H₀: μ ≤ 10;vs.H_A: μ > 10,we reject H₀ at level of significance α 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.

Question 75

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 whether 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 value of the test statistic to test the claim?

Question 76

A recent study conducted by the state government attempts to determine whether the voting public supports a 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 to test the claim at α = .10?

Question 77

For the following hypothesis test,where H₀: μ ≤ 10;vs.H_A: μ > 10,we reject H₀ at level of significance α 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.

Question 78

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 to test the claim at α = .01?

Question 79

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 80

Determine the p-value for H₀: μ = 95;versus H_A: μ ≠ 95,when