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Statistics and statistical analysis provide the ability to test a hypothesis and make a determination about a population with certainty based on a sample. (1 pt)

Select one:

True

False

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Which statement is true about the level of significance? (1 pt)

Select one:

a. It is the probability of being wrong.

b. It is the maximum probability of failing to reject the null hypothesis when it is true.

c. It is the maximum probability of rejecting the null hypothesis when it is true

d. It is the maximum probability of failing to reject the null hypothesis when it is false.

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Refer to the decision chart (Figure 8-25) in the Bluman text (page 394 of 3rd edition, page 421 of 4th edition). The chart helps you decide when to use a Z or t- test. The t-test is appropriate when:
(1 pt)

Select one:

a. "s" < sigma (sample standard deviation is less than population standard deviation).

b. the sample size is small (<30) but the population size is large (>100).

c. the population standard deviation is unknown and the sample is small (<30). (We compute a standard deviation from that small sample to substitute into test value computations.)

d. Every third leap year (don't pick this one - haha).

e. "s" = sigma (sample standard deviation equals population standard deviation).

f. the sample is small (<30) regardless of whether we have a population standard deviation available.

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Look up the t-table value (critical value) given alpha equal .05, a one-tailed test, and a sample size of 25.

Remember, the t-table uses degrees of freedom for the row definition, which for purposes of this course is generally sample size minus 1.

Be careful with the column header as well. This is a one-tailed test.

Provide your answer to 2 decimal places.

(1pt.)

Answer:

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Compute the Z-Statistic to test a mean, given:

Sample Mean = 80

Population Mean = 75

Population Standard Deviation (sigma) = 8

n (sample size) = 16

(Provide your answer to one decimal place.) (1 pt.)

Answer:

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Compute the t-Statistic to test a mean, given:

Sample Mean = 800

Population Mean = 810

Sample Standard Deviation = 8

n (sample size) = 16

(Provide your answer to one decimal place.) (1 pt.)

Answer:

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At a monthly symposium, the long term average registration has been 900 attendees, with a standard deviation of 40 attendees. The average registration for the 16 symposia held so far the last two years is 850. At = 0.05, test whether registration for the past two years is different from previous experience.

Hypothesis form: Because we see the word "different" no sign is implied for hypothesis testing, and we have a two-tailed test.

Ho = 900, H1 <> 900

Statistic: This problem uses the z-statistic because the standard deviation comes from the population of all symposia, not just those held this year. Even though the sample is small, (16 symposia, <30) we use the z-statistic because we have a population standard deviation available.

1) Find the critical value for the Z-statistic using the Standard Normal table.

2) Compute the test Z-statistic and compare it to the critical value.

3) Indicate whether you accept or reject the Null Hypothesis.

Make the appropriate selection for parts 1, 2, and 3, from the choices below.

(3 pts.)

Select one:

a. 1.65, 4, Reject Null Hypothesis

b. 1.65, 4, Don't Reject Null Hypothesis

c. 1.65, 5, Reject Null Hypothesis

d. 1.65, 5, Don't Reject Null Hypothesis

e. 1.96, 4, Reject Null Hypothesis

f. 1.96, 4, Don't Reject Null Hypothesis

g. 1.96, 5, Reject Null Hypothesis

h. 1.96, 5, Don't Reject Null Hypothesis

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At a monthly medical symposium, the long term average registration has been 900 attendees. The average registration for the 9 symposia held so far this year is 850, with a standard deviation of 15. At = 0.05, test whether registration for this year is different from previous years?

Hypothesis form: Because we see the word "different" no sign is implied for hypothesis testing, and we have a two-tailed test.

Ho = 900, H1 <> 900

Statistic: This problem uses the t-statistic because the standard deviation comes from the sample of this year's 9 symposia, and the sample is small < 30.

1) Find the critical value for t-statistic from the t-table.

2) Compute the t-test value from the data given and compare to the critical value.

3) Indicate whether you reject or do not reject the Null Hypothesis.

Make the appropriate selection for parts 1, 2, and 3, from the choices below.

(3 pts.)

Select one:

a. 2.306, 5, Reject Null Hypothesis

b. 2.306, 5, Do Not Reject Null Hypothesis

c. 2.306, 10, Reject Null Hypothesis

d. 2.306, 10, Do Not Reject Null Hypothesis

e. 2.262, 5, Reject Null Hypothesis

f. 2.262, 5, Do Not Reject Null Hypothesis

g. 2.262, 10, Reject Null Hypothesis

h. 2.262, 10, Do Not Reject Null Hypothesis

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Hypothetical Question: Mature Coastal Alaskan Brown Bears are well studied. Males weigh about 800 pounds on average, with a standard deviation of 50 pounds. Assume a sample of 25 such bears living near Hoonah Alaska yields an average weight of 825 pounds. A test of means will determine if the Hoonah sub-population average weight is different than the average weight of the general Alaskan population.  How would you conduct the test? (Hint: Refer to the decision chart (Figure 8-25) of the Bluman text.
(1 pt)

Select one:

a. I have a small sample (less than 30 bears). I always use the t-test in small sample situations, and will obtain a standard deviation from my sample to conduct the test.

b. I have an applicable population standard deviation, and always use the Z test when I have a population standard deviation regardless of sample size.

c. I don't have a population standard deviation, but I do have a sample of 30 bears or more, so I use the Z test and obtain a standard deviation from my sample to conduct the test.

d. I don't have a population standard deviation, and have a small sample (less than 30 bears). I must use the t-test to correct for the small sample size, and will obtain a standard deviation from my sample to conduct the test.

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The Food and Drug Administration (FDA) tests a newly developed drug to determine if it is better than the existing standard medication which has a 10% cure rate. The FDA conducts the following test.

Ho: New drug cure rate is less than or equal to 10%

Ha: New drug cure rate is greater than 10%

A Type I Error occurs when we reject a null hypothesis when it is in fact true.

In this case a Type I error occurs if the FDA:

(1 pt)

Select one:

a. determines the new drug has no better than a 10% cure rate, when in fact the cure rate is better than 10%.

b. determines the new drug has no better than a 10% cure rate, and in fact the cure rate is no better than 10%.

c. determines the new drug has better than a 10% cure rate, and in fact the cure rate is better than 10%.

d. determines the new drug has better than a 10% cure rate, when in fact the cure rate is no better than 10%.

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The Food and Drug Administration (FDA) tests a newly developed drug to determine if it is better than the existing standard medication which has a 10% cure rate. The FDA conducts the following test.

Ho: New drug cure rate is less than or equal to 10%  

Ha: New drug cure rate is greater than 10%

A Type II Error occurs when we do not reject a false null hypothesis. In this case a Type II error occurs if the FDA:

(1 pt)

Select one:

a. determines the new drug has better than a 10% cure rate, when in fact the cure rate is no better than 10%.

b. determines the new drug has better than a 10% cure rate, and in fact the cure rate is better than 10%.

c. determines the new drug has no better than a 10% cure rate, and in fact the cure rate is no better than 10%.

d. determines the new drug has no better than a 10% cure rate, when in fact the cure rate is better than 10%

Explanation / Answer

1) Statistics and statistical analysis provide the ability to test a hypothesis and make a determination about a population with certainty based on a sample.

this statement is true because in statistics we have different methods to check the availability of the data according to the hypothesis, also by applying t test, chi square test we can get the result based on the hypothesis.

hence true.

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