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Q:
In testing H0: p .33; versus HA: p < .33 using the critical value rule, with = .20 and n = 100, what is the value of the test statistic?
Q:
In testing H0: p = .2; versus HA: p .2 using the critical value rule, with = .26 and n = 100, what is the value of the test statistic?
Q:
In testing H0: 23; versus HA: > 23 using the critical value rule, when = 26, = 6, and n = 30, what is the value of the test statistic?
Q:
In testing H0: = 23; versus HA: > 23 using the critical value rule, when = 26, s = 6, and n = 20, what is the value of the test statistic?
Q:
To apply the p-value rule, determine the p-value for H0: p = .5; versus HA: p .5, when n = 225 and = .54.
Q:
Determine the p-value for H0: p .5; versus HA: p > .5, when n = 225 and = .54.
Q:
When computing a 95 percent confidence interval for 2 with a sample of n = 30, what values of x2 would we use in the calculations?A. 45.7222 and 16.0471B. 46.9792 and 16.7908C. 42.5569 and 17.7083D. 43.7729 and 18.4926
Q:
The value of x2 in a particular situation depends onA. the left-hand tail area .B. the number of degrees of freedom.C. the right-hand tail area .D. the left-hand tail area and the number of degrees of freedom.E. the number of degrees of freedom and the right-hand tail area .
Q:
For the following hypothesis test, where H0: 10; vs. HA: > 10, we reject H0 at level of significance 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 haveA. made a Type I error.B. made a Type II error.C. made a correct decision.D. increased the power of the test.
Q:
For the following hypothesis test, where H0: 10; vs. HA: > 10, we reject H0 at level of significance 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 haveA. made a Type I error.B. made a Type II error.C. made a correct decision.D. increased the power of the test.
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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.
Q:
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
Q:
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 < .66B. p > .66C. p = .66D. p .66
Q:
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 .66B. p > .66C. p .66
Q:
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
Q:
The value of the test statistic is compared with a(n) _______________ in order to decide whether the null hypothesis can be rejected.A.B.C. p-valueD. critical value
Q:
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. B. C. p-valueD. Type I error
Q:
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
Q:
The ____________ hypothesis is not rejected unless there is sufficient sample evidence to do so.
A. research
B. alternative
C. null
D. true
Q:
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
Q:
As the Type II error, ,of a statistical test increases, the power of the test _____________.A. increasesB. decreasesC. stays the sameD. randomly fluctuates
Q:
Assuming a fixed sample size, as (Type I error) decreases, (Type II error) ___________.A. increasesB. decreasesC. stays the sameD. randomly fluctuates
Q:
For a fixed sample size, the lower we set , the higher is the ___________.A. Type I errorB. Type II errorC. random errorD. p-value
Q:
____________ is not rejecting H0 when H0 is false.A. A Type I errorB. A Type II errorC. The random errorD.
Q:
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
Q:
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
Q:
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
Q:
Rejecting a true null hypothesis is called a ______________ error.A. Type IB. Type IIC. RandomD.
Q:
Using a x2 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 , we can conclude that the new process is more consistent than the current process.
Q:
When evaluating a new process, using the square root of the upper end of the confidence interval for 2 gives an estimate of the smallest that for the new process might reasonably be.
Q:
To compute a 95 percent confidence interval for 2, we use n - 1 degrees of freedom and the chi-square points on the distribution curve of x2/2 and of x21-(/2).
Q:
In order to make statistical inferences about 2 that are valid using a chi-square distribution, the assumption is that the sampled population is also a chi-square distribution.
Q:
x2 is the point on the vertical axis under the curve of the chi-square distribution that gives a right-hand tail area equal to .
Q:
The exact shape of the chi-square distribution depends on the degrees of freedom.
Q:
The chi-square distribution is a continuous probability distribution that is skewed to the left.
Q:
The power of a statistical test is the probability of rejecting the null hypothesis when it is false.
Q:
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.
Q:
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 = .05, we would reject the null hypothesis.
Q:
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 = .10, we would not reject H0.
Q:
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 = .01, we can reject the null hypothesis.
Q:
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 = .05, we do not reject H0.
Q:
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 HA: > 100. (Assume the population is normally distributed.)
Q:
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: = 100.
Q:
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 = .76. The sample evidence indicates that the average time is less than 3 years and is significant at = .01.
Q:
We are testing H0: 42; versus HA: > 42. When = 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.)
Q:
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.
Q:
We are testing H0: 2.5; versus HA: < 2.5. When = 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.)
Q:
We test H0: 3.0; versus HA: > 3.0. If = 3.44, s = .57, and n = 13, at a significance level of .05, we do not reject H0. (Assume population normality.)
Q:
We are testing H0: p .7; versus HA: p < .7. With = .63 and n = 100, at = .01, we do not reject the null hypothesis.
Q:
We are testing H0: .95; versus HA: > .95. When = .99, s = .12, and n = 24, at alpha = .05, we reject H0. (Assume a normally distributed population.)
Q:
After testing H0: p = .33; versus HA: p < .33; at = .05, with = .20 and n = 100, we do not reject H0.
Q:
When we test H0: p = .2; versus HA: p .2, with = .26 and n = 100, at alpha = .05, we reject the null hypothesis.
Q:
We are testing H0: = 32; versus HA: > 32. If = 36, s = 1.6, and n = 30, at = .05, we should reject H0.
Q:
We are testing H0: 22; versus HA: < 22. Given = .01, n = 100, = 21.431, and = 1.295, we should not reject H0.
Q:
We are testing H0: 8; versus HA: > 8. Given = .01, n = 25, = 8.112, and s = .16, we should reject the H0. (Assume the sample is selected from a normally distributed population.)
Q:
When the null hypothesis is true, there is no possibility of making a Type I error.
Q:
When the null hypothesis is not rejected, there is no possibility of making a Type I error.
Q:
When applying either the critical value rule or the p-value rule about a single mean, reducing the level of significance () will increase the size of the rejection region.
Q:
The level of significance, , indicates the probability of rejecting a false null hypothesis.
Q:
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, , from .05 to .10 will reduce the probability of a Type II error.
Q:
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, , from .05 to .10 will reduce the probability of a Type I error.
Q:
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.
Q:
As the level of significance, α, increases, we are more likely to reject the null hypothesis.
Q:
The null hypothesis is a statement that will be accepted only if there is convincing sample evidence that it is true.
Q:
Everything else being constant, increasing the sample size decreases the probability of committing a Type II error.
Q:
Alpha () is the probability that the test statistic would assume a value at or more extreme than the observed value of the test.
Q:
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.
Q:
You cannot make a Type II error when the null hypothesis is true.
Q:
A Type II error is failing to reject a false null hypothesis.
Q:
The larger the p-value, the more we doubt the null hypothesis.
Q:
A Type I error is rejecting a true null hypothesis.
Q:
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.