AP Statistics - Test 6

Workshop Statistics Activities 21-25

BPS Chapter 6.1, 6.2, 7.2

Mr. Coons

Except for the multiple choice questions below (1-3) and the last problem, all work and answers must be on separate paper. |

1. **Circle the correct answer: **To find confidence
intervals for the mean of a normal distribution, the t distribution is usually
used instead of the standard normal distribution because:

- a) the mean of the population is not known

b) the t distribution is more efficient

c) the variance of the population is usually not known

d) the standard error of the estimate is s/sqrt(n)

e) the sample mean is known.

2.

- a) The normal distribution is symmetrical while
the t-distributions are slightly skewed.

- b) The proportion of area beyond a specific value
of t is less than the proportion of area beyond the corresponding value
of z.

- c) The greater the df, the more the t-distributions
resemble the standard normal distribution.

- d) All of the above.

- e) None of the above.

3. **Circle the correct answer: **Suppose that
a significance test is such that the P-value does not change very much when
the assumptions of the procedures are violated. What is such a test called?

a. a

t-test

b. a test with

high power

c. a

highly significanttest

d. a

robusttest

4. Blood pressure can be classified as low, normal, and high. A SRS of 40 regular blood donors revealed that 12 of them had low blood pressure. An SRS of 40 people who have never donated blood finds 5 of the 40 had low blood pressure. The difference of these two proportions is statistically significant at the 1% level.

In order to promote blood donation, a local chapter of The Red Cross quotes this study and suggests people lower their blood pressure by becoming regular blood donors. Explain why this type of study cannot be used to support such a claim.

5. In an experiment, the mean of the monthly salaries of a sample of men was $4000 and the salaries had standard deviation $270. The standard error of the mean of these salaries was $90. What was the sample size? Show your work.

6. An SRS of 100 of a certain popular model car
in 1993 found that 11 had a certain minor defect in the brakes. An SRS of
120 of this model car in 1994 found that 30 had the minor defect in the
brakes. We are interested in comparing the proportion of all cars of this
model in 1993 and 1994, respectively, that actually contain the defect.

a. Using the above data, and showing your work, compute the pooled sample proportion of defects.

b. In step c below, you will be asked to compute a 95% confidence interval for this problem. Clearly explain why the pooled sample proportion you computed in step a will or will not be used in this computation.

c. Compute by hand showing your steps so it is clear that you are working without the test feature of your calculator a 95% confidence interval for this problem.

d. Interpret this interval in terms of the problem (do not consider duality).

e. What would be the name of an appropriate test of significance to apply to this problem?

f. State an appropriate hull hypothesis for a test of significance for this problem and determine the results of that test of significance solely from the confidence interval you computed in step c.

g. Are the appropriate assumptions satisfied in order to do the appropriate test of significance for the given problem? Support your answer.

7. Since most people are right-handed, a company
that designs machinery has traditionally placed the controls that demand
the most hand strength so that they will be used by the right hand.company
decides that it should test its assumption that the right hand of right-handed
adults tends to be stronger than the left hand.right-handed adults are selected
from employees of this company for the test.strength is measured by using
a calibrated hand gripper. The people test their left hand first and then
their right hand.hand strengths, in kilograms, for each person are given
below.

**DO NOT TYPE IN THIS DATA. IT IS AVAILABLE FROM
YOUR TEACHER.
**

Person | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

Right Hand | 11.7 | 12.7 | 11.4 | 10.2 | 12.2 | 11.3 | 11.1 | 11.7 | 11.7 |

Left Hand | 11.6 | 11.2 | 10.6 | 11.2 | 10.9 | 10.9 | 10.7 | 10.3 | 10.5 |

a. Briefly discuss a concern that is particular to the design of this
study (not assumptions for a test of significance.

b. Are the samples independent or dependent? Explain why this decision
is important?

c. Demonstrate you can do the following BY HAND and with tables. You must show formulas and the substitution of values into the formulas. However, standard deviation(s) or stand error(s) can be determined from the calculator. See your teacher if you are not sure what you can do.

Do a **fully annotated** test of significance to determine if these
data support the conclusion that the right hand of right-handed adults tends
to be stronger than the left hand.

8. In assessing the weather prior to leaving our residences on a spring morning, we make an informal test of the hypothesis "The weather will be fair today."the "best" information available to us, we complete the test and dress accordingly.would be the consequences of a Type I and Type II error?

**From the choices below select and clearly explain your choice of the
correct answer. You may answer on this sheet.
**

a) Type I error: inconvenience in carrying needless rain equipment

Type II error: clothes get soaked

b) Type I error: clothes get soaked

Type II error: inconvenience in carrying needless rain equipment

c) Type I error: clothes get soaked

Type II error: no consequence since Type II error cannot be made

d) Type I error: no consequence since Type I error cannot be made

Type II error: inconvenience in carrying needless rain equipment