Deck 9: Hypothesis Testing

Question 1

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

Answer 1

False

Question 2

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.

Answer 2

True

Question 3

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.

Answer 3

False

Question 4

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

Question 5

A Type I error is rejecting a true null hypothesis.

Question 6

We are testing H₀: μ ≤ 8;versus H_A: μ > 8.Given α = .01,n = 25, = 8.112,and s = .16,we should reject the H₀.(Assume the sample is selected from a normally distributed population. )

Question 7

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

Question 8

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

Question 9

We are testing H₀: μ ≥ 22;versus H_A: μ < 22.Given α = .01,n = 100, = 21.431,and σ = 1.295,we should not reject H₀.

Question 10

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

Question 11

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

Question 12

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 13

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

Question 14

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 15

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 16

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

Question 17

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

Question 18

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 19

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 20

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

Question 21

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 22

The HR department tested how long employees stay 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 23

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 24

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

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 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 27

We are testing H₀: μ ≥ 2.5;versus H_A: μ < 2.5.When = 2.46,s = .05,and n = 26,at α = .10 we reject the null hypothesis.(Assume that the population from which the sample is selected is normally distributed. )

Question 28

We are testing H₀: μ = 32;versus H_A: μ > 32.If = 36,s = 1.6,and n = 30,at α = .05,we should reject H₀.

Question 29

The chi-square distribution is a continuous probability distribution that is skewed to the left.

Question 30

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 31

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

Question 32

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 33

We are testing H₀: μ ≤ .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 34

The exact shape of the chi-square distribution depends on the degrees of freedom.

Question 35

We are testing H₀: p ≥ .7;versus H_A: p< .7.With = .63 and n = 100,at α = .01,we do not reject the null hypothesis.

Question 36

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 = .05,we would reject the null hypothesis.

Question 37

We test H₀: μ ≤ 3.0;versus H_A: μ > 3.0.If = 3.44,s = .57,and n = 13,at a significance level of .05,we do not reject H₀.(Assume population normality. )

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 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 39

When we test H₀: p = .2;versus H_A: p ≠ .2,with = .26 and n = 100,at alpha = .05,we reject the null hypothesis.

Question 40

After testing H₀: p = .33;versus H_A: p< .33;at α = .05,with = .20 and n = 100,we do not reject H₀.

Question 41

In order to make statistical inferences about σ² that are valid using a chi-square distribution,the assumption is that the sampled population is also a chi-square distribution.

Question 42

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 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)True

Question 44

χ²_α is the point on the vertical axis under the curve of the chi-square distribution that gives a right-hand tail area equal to α.

Question 45

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 46

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

A)Type I
B)Type II
C)Random
D)β

Question 47

When evaluating a new process,using the square root of the upper end of the confidence interval for σ² gives an estimate of the smallest that σ for the new process might reasonably be.

Question 48

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

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

Question 49

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 50

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 51

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 52

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 53

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

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

Question 54

To compute a 95 percent confidence interval for σ²,we use n - 1 degrees of freedom and the chi-square points on the distribution curve of χ_α/2² and of χ_1-(α/2)².

Question 55

____________ 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 56

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 57

Using a χ² test statistic to test the null hypothesis that the variance of a new process is equal to the variance of the current process and rejecting at a p-value less than α,we can conclude that the new process is more consistent than the current process.

Question 58

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 59

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 60

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 61

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 62

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 63

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 64

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 65

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 66

Determine the p-value for H₀: p = .5;versus H_A: p ≠ .5,when n = 225 and = .54.

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

The value of χ²_α in a particular situation depends on:

A)The left-hand tail area α.
B)The number of degrees of freedom.
C)The right-hand tail area α.
D)The left-hand tail area α and the number of degrees of freedom.
E)The number of degrees of freedom and the right-hand tail area α.

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

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 71

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 72

When computing a 95 percent confidence interval for σ² with a sample of n = 30,we would use the following values of χ² in the calculations:

A)45.7222 and 16.0471
B)46.9792 and 16.7908
C)42.5569 and 17.7083
D)43.7729 and 18.4926

Question 73

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 74

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 75

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 76

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 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 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 78

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 79

Determine the p-value for H₀: p ≤ .5;versus H_A: p> .5,when n = 225 and = .54.

Question 80

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