Deck 9: Hypothesis Testing

Question 1

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.

Answer 1

True

Question 2

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.

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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

Question 5

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 6

When applying either the critical value rule or the p-value rule about a single mean,reducing the level of significance (α)will increase the size of the rejection region.

Question 7

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

Question 8

When applying either the critical value rule or the p-value rule 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 9

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

Question 10

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

Question 11

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 12

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

Question 13

Using the p-value rule for a population proportion or mean,if the level of significance is less than the p-value,the null hypothesis is rejected.

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

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 16

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

Question 17

A Type I error is rejecting a true null hypothesis.

Question 18

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

Question 19

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

Question 20

When applying either the critical value rule or the p-value rule 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 21

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 22

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 23

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 24

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

Question 25

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 26

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

Question 27

Based on a random sample of 25 units of product X,the average weight is 102 lb and the sample standard deviation is 10 lb.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 lb.Assume the population is normally distributed.Using the critical value rule,at α = .05,we do not reject H₀.

Question 28

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 29

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 1,500 voting age citizens.1,020 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.Using the critical value rule,at α = .05,we would reject the null hypothesis.

Question 30

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

Question 31

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 32

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 33

Based on a random sample of 25 units of product X,the average weight is 102 lb and the sample standard deviation is 10 lb.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 lb.Assume the population is normally distributed.Using the critical value rule,at α = .01,we can reject the null hypothesis.

Question 34

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 35

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 36

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

Question 37

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 1,500 voting age citizens.1,020 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.Using the critical value rule,at α = .10,we would not reject H₀.

Question 38

Based on a random sample of 25 units of product X,the average weight is 102 lb and the sample standard deviation is 10 lb.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 lb.Therefore,the alternative hypothesis can be written as H_A: μ > 100.(Assume the population is normally distributed. )

Question 39

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.Historically,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 using the critical value rule,we can show that the completion time has increased.

Question 40

Based on a random sample of 25 units of product X,the average weight is 102 lb and the sample standard deviation is 10 lb.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 lb.Assume the population is normally distributed.Therefore,one way of expressing the null hypothesis is H₀: μ = 100.

Question 41

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 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

____________ is not rejecting H₀ when H₀ is false.

A) A Type I error
B) A Type II error
C) The random error
D) α

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

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 46

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 1,500 voting age citizens.1,020 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 47

Rejecting a true null hypothesis is called a ______________ error.

A) Type I
B) Type II
C) Random
D) β

Question 48

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 49

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 50

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 51

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 52

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 53

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 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 χ²_α/2 and of χ²_1−(α/2).

Question 55

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 56

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 57

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 58

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 59

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 when applying the p-value rule,we are rejecting at a p-value less than α,we can conclude that the new process is more consistent than the current process.

Question 60

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

A) research
B) alternative
C) null
D) true

Question 61

Using the critical value rule,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 manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line.The machine that dispenses dressing is working properly when 8 ounces are dispensed.The standard deviation of the process is 0.15 ounces.A sample of 48 bottles is selected periodically,and the filling line is stopped if there is evidence that the mean amount dispensed is different from 8 ounces.Suppose that the mean amount dispensed in a particular sample of 48 bottles is 7.983 ounces.Calculate a confidence interval to test the hypotheses at α = .05 and determine if the process should be stopped.

Question 63

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 1,500 voting age citizens.1,020 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 alternative hypothesis?

A) p < .66
B) p > .66
C) p = .66
D) p ≤ .66

Question 64

It has been hypothesized that,on average,employees spend one hour a day playing video games at work.To test this at her company,a manager takes a random sample of 35 employees,who showed a mean time of 55 minutes per day,with an assumed population standard deviation of 5 minutes.Calculate the test statistic.

Question 65

Using either the critical value rule or the p-value rule,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 66

A baker must monitor the temperature at which cookies are baked.Too much variation will cause inconsistency in the texture of the cookies.Past records show that the variance of the temperatures has been 1.44 degrees.A random sample of 30 batches of cookies is selected,and the sample variance of the temperature is 4.41 degrees.What is the 95 percent confidence interval for σ² at α = .05?

Question 67

Using either the critical value rule or the p-value rule,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 68

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 69

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 70

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 71

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 72

Using the p-value rule,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

Using the p-value rule,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 74

Using the critical value rule,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 75

Using the p-value rule,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 76

The manager of a grocery store wants to determine whether the amount of water contained in 1-gallon bottles purchased from a nationally known manufacturer actually averages 1 gallon.It is known from the specifications that the standard deviation of the amount of water is equal to 0.02 gallon.A random sample of 32 bottles is selected,and the mean amount of water per 1-gallon bottle is found to be 0.995 gallon.Calculate a confidence interval to test the hypotheses at α = .001 and determine whether the specifications are being met.

Question 77

A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line.The machine that dispenses dressing is working properly when 8 ounces are dispensed.The standard deviation of the process is 0.15 ounces.A sample of 48 bottles is selected periodically,and the filling line is stopped if there is evidence that the mean amount dispensed is different from 8 ounces.Suppose that the mean amount dispensed in a particular sample of 48 bottles is 7.983 ounces.Calculate the p-value and determine if the process is working properly when testing at α = .10 using the p-value rule.

Question 78

The manager of a grocery store wants to determine whether the amount of water contained in 1-gallon bottles purchased from a nationally known manufacturer actually averages 1 gallon.It is known from the specifications that the standard deviation of the amount of water is equal to 0.02 gallon.A random sample of 32 bottles is selected,and the mean amount of water per 1-gallon bottle is found to be 0.995 gallon.Calculate the test statistic.

Question 79

The manager of a grocery store wants to determine whether the amount of water contained in 1-gallon bottles purchased from a nationally known manufacturer actually averages 1 gallon.It is known from the specifications that the standard deviation of the amount of water is equal to 0.02 gallon.A random sample of 32 bottles is selected,and the mean amount of water per 1-gallon bottle is found to be 0.995 gallon.Calculate the p-value and test whether the specifications are being met at α = .001 using the p-value rule.

Question 80

A Type II error is defined as ________________ 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