Question

1.In a test of the difference in mean incomes of males and females employed in

the same positions p< .20. This means

A. In a t test of the difference between two means you would conclude there is a

difference if alpha=.05

B. In a t test of the difference between two means you would conclude there is a

difference if alpha=.10

C. You would conclude there is a difference only if you were willing to risk a very

large chance of making a Type I error

D. The difference between men and women’s incomes is less than 20%

2. If you conclude that there is no difference in the average achievement test

scores of students in large vs. small classes of the same subject, the probability

that you are making an error is

A. alpha

B. (1- alpha)

C. small if there is only a small difference in the test scores

D. large if the sample size is large

E. large if there is only a small difference in the test scores

3. The probability of determining that there is a difference in the average

achievement scores of students in large vs. small classes of the same subject

when there is no real difference is

A. (1-beta)

B. (1-alpha)

C. beta

D. dependent on your sample size

E. alpha

4. If you measured the average household expenditures on groceries for a

random sample of 50 families in the year 2005 and for those same families again

in 2015 df for a hypothesis test of the difference would be

A. 99

B. 98

C. 50

D. 48

E. 49

5. You want to compare the average number of copies available from two

brands of ink cartridges by comparing the comparing the number of copies from

75 printers using the first brand then replacing those cartridges and determining

the number of copies for those same 75 printers using the second brand. Df

would be

A. 74

B. 148

C. 149

D. 73

E. 150

6. If you were to calculate a confidence interval estimate for the average

difference between the m.p.g. obtained with high octane minus regular gas for a

sample of cars that gave you LCL= (-2) and UCL= 3, you would know

A. the average difference is 5 m.p.g.

B. there may be no difference at all

C. high octane gives you better mileage than regular gas

D. regular gas gives you better mileage than high octane

E. the difference could be as much as 10 m.p.g.

7. If you were to administer a test of short term memory in the form of random

number recall to a random group of 40 adults and calculated their average recall

scores and compared that average to the average recall of a different group of

forty adults who had been engaged in a memory training program, assuming

equal population variances, df would be

A. 80

B. 89

C. 38

D. 39

E. 78

8. A research article investigating the difference between two different

approaches to teaching social skills to autistic adults reports p=.041. You would

conclude

A. There is a difference using alpha=.01

B. There may be no difference using alpha=.05

C. There may be no difference using alpha=.10

D. There is a difference using alpha=.001

E. There is a difference using alpha=.05

9. An F test for equal variances yields p=.377

A. You would do a t test assuming equal variances

B. You would do a t test assuming unequal variances.

10. If the “power” of a statistical test =.80 that means

A. There is a 20% chance of being wrong andrejecting the null when it is true

B. There is a 80% chance you will be right and reject the null when it is false

C. There is a an 80% chance you will be wong and not reject a false null

D. There is a 20% chance you will be right and not reject the null when it is true

E. There is an 80% chance that you will be right in whatever decision you make

Answer 1

1.In a test of the difference in mean incomes of males and females employed in

the same positions p< .20. This means

Null hypothesis: No difference in the mean incomes of men and women.

Alternative hypo: There is a difference in the mean incomes of men and women.

p-value is the null hypothesis being true.

So here p < 0.20 means the probability that there is no difference in the mean incomes of men and women is less than 20%.

A. In a t test of the difference between two means you would conclude there is a

difference if alpha=.05

we reject the null hypothesis when p < alpha, here we know that p < 0.20 but here it can be anything between 0 - 0.20.

B. In a t test of the difference between two means you would conclude there is a

difference if alpha=.10

we reject the null hypothesis when p < alpha, here we know that p < 0.20 but here it can be anything between 0 - 0.20.

C. You would conclude there is a difference only if you were willing to risk a very

large chance of making a Type I error

this again relates to alpha where type 1 error = alpha = probability of rejecting the null hypothesis when it is true, here if we are taking the alpha to more than 0.20, cause only then we will be able to reject the null hypothesis thus might make a type 1 error. This is a very large value for alpha.

D. The difference between men and women’s incomes is less than 20%

It is the null hypothesis being true, so its a probability not a value of difference.

2. If you conclude that there is no difference in the average achievement test

scores of students in large vs. small classes of the same subject, the probability

that you are making an error is

Concluding no difference means we are accepting the null hypothesis. Therefore there is a chance of making type 2 errorr which is the probability of accepting a false null hypothesis. It is denoted by

A. alpha

probabiltiy of making type 1 error.

B. (1- alpha)

probabiltiy of correctly accepting the null hypothesis.

C. small if there is only a small difference in the test scores

If the sample is large then the decision can be accurate thus a small difference can be allowed and error of the decision of accepting the null can be small.

D. large if the sample size is large

Larger the sample more is the accuracy there less is the chance of error.

E. large if there is only a small difference in the test scores

If there is small difference, we can allow little difference as we do when we calculate the p-value.

3. The probability of determining that there is a difference in the average

achievement scores of students in large vs. small classes of the same subject

when there is no real difference is

We are concluding that there is a difference (rejecting the null hypo) but in reality there is no difference (nul hypothesis is true).

So here we are making type 1 error of rejecting a true null hypo. Therefore type 1 is denoted by

A. (1-beta)

probabiltiy of correctly rejecting the null hypo

B. (1-alpha)

probabiltiy of correctly accepting the null hypo

C. beta

probabiltiy of incorrectly accepting the null hypo

D. dependent on your sample size

E. alpha

4. If you measured the average household expenditures on groceries for a

random sample of 50 families in the year 2005 and for those same families again

in 2015 df for a hypothesis test of the difference would be

It is the same families therefore the test will be for average after calculating each individual difference. It is an example of dependent t-test.

Therefore df = n - 1 = 50 - 1

A. 99

B. 98

C. 50

D. 48

E. 49

5. You want to compare the average number of copies available from two

brands of ink cartridges by comparing the comparing the number of copies from

75 printers using the first brand then replacing those cartridges and determining

the number of copies for those same 75 printers using the second brand. Df

would be

Here we are comparing two separate brands of ink and not the printer's ability so even though the printer is same we will have independent t-test for difference in the mean.

df = n1 + n2 - 2 = 75copies of 1st brand + 75 of 2nd - 2

A. 74

B. 148

C. 149

D. 73

E. 150

6. If you were to calculate a confidence interval estimate for the average

difference between the m.p.g. obtained with high octane minus regular gas for a

sample of cars that gave you LCL= (-2) and UCL= 3, you would know

Here the confidence interval is for the range of values the average difference can take, since here it is (-2 , 3 ) so the avg. difference can take any values within the range. It is uncertain because we can only be 95%, 99%, 90% confident and never 100%.

A. the average difference is 5 m.p.g.

B. there may be no difference at all

since the range has '0', we can say that the difference is '0' that is no difference.

C. high octane gives you better mileage than regular gas

D. regular gas gives you better mileage than high octane

E. the difference could be as much as 10 m.p.g.

Experts are supposed to solve the first 4 compulsorily under company rules and rest at the option of the expert.