STAtistics / Mr. Hansen
2/10/2006

Name: _________________________

Test #5

Probability, Type I/Type II error, sampling distributions, and simulations

Time limit: 34 minutes (51 for extended time).

 

Useful Formulae:

 

 

 

P(A È B) = P(A) + P(B) – P(A Ç B)

 



 

E(X) = mX = S xi pi

 

 

 

 

If X has a binomial distribution with parameters n and p, then:

 

 







If X has a normal distribution with mean m and standard deviation s, then:

 

 

 

 

 

 

 

 

Inferential Statistics

 

Standardized statistic:



Confidence interval:

 

 

 

 

1.

Suppose that there is a population from which we will plan to take a random sample. What term have we been using for the distribution of data in the population?

 

(A) underlying data distribution
(B) histogrammic distribution
(C) sample distribution

(D) sampling distribution
(E) sample statistic

 

 

 

2.

A t distribution with df = 20 has what shape?

 

(A) normal (z)
(B) almost normal, except with more “flab” in the tails
(C) bimodal
(D) binomial
(E) skew left or skew right, depending on the value of df

 

 

3.

The abbreviation df stands for _____ and equals _____ in the case of the sampling distribution of  (single sample).

 

(A) degrees of freedom, n – 1
(B) degrees of freedom, n
(C) distribution of factors, n – 1

(D) distribution of factors, n
(E) distribution of factors, n + 1

 

 

4.

How are the sampling distribution of  (single sample) and the sampling distribution of  (single sample) most accurately described?

 

(A) t and normal, respectively
(B) t and t, respectively
(C) t and binomial, respectively

(D) binomial and t, respectively
(E) binomial and normal, respectively

 

 

5.

The Student’s t distribution came from what field?

 

(A) tobacco
(B) education
(C) illegal drugs

(D) brewing
(E) pornography

 

 

6.

We poll an SRS of 500 voters in a large city and discover that 322 of them think that Candidate Jones is supercilious. A writer for the city newspaper estimates that the true proportion of voters in the city who think Candidate Jones is supercilious is between 60% and 65%. With what confidence can she make this statement?

 

(A) 55%
(B) 59%
(C) 62.5%

(D) 68%
(E) 95%

 

 

7.

By default (i.e., unless otherwise stated), political polls in The Washington Post that are reported with a margin of error have a confidence level of . . .

 

(A) 90%
(B) 95%
(C) 99%

(D) 99.9%
(E) 100%

 

 

8.

I hope that my true mean diastolic blood pressure is no more than 80 mm Hg. Over a period of time, I take 5 measurements at random intervals and find a mean of 78 mm Hg with a standard deviation of 6 mm Hg. With what confidence can I assert that my true mean diastolic blood pressure is less than or equal to 80 mm Hg?

 

(A) 63%
(B) 68%
(C) 84%

(D) 98%
(E) none of these, since 5 is too small a sample size to use with the z approximation

 

 

9.

I hope that my true mean diastolic blood pressure is no more than 80 mm Hg. Over a period of time, I take 40 measurements at random intervals and find a mean of 78 mm Hg with a standard deviation of 6 mm Hg. With what confidence can I assert that my true mean diastolic blood pressure is less than or equal to 80 mm Hg?

 

(A) 63%
(B) 68%
(C) 84%

(D) 98%
(E) none of these, since 40 is too small a sample size to use with the z approximation

 

 

10.

The four themes of our course are exploratory data analysis, design of studies, probability, and _____ , and the latter can be summarized as _____ .

 

(A) hypothesis testing, computing probabilities of Type I and Type II errors
(B) inferential statistics, computing probabilities of Type I and Type II errors
(C) hypothesis testing, using sampling distributions to compute statistics
(D) inferential statistics, computing probabilities of Type I and Type II errors
(E) inferential statistics, using statistics to estimate parameters or to make decisions regarding hypotheses

 

 

11.

If 4 cards are drawn without replacement from a well-shuffled deck, compute the probability that there is exactly one pair (not two pair, not 3 of a kind, not 4 of a kind).

 

(A)
(B)
(C)

(D)
(E)

 

 

 

 

 

 

12.

In a screening test for high blood pressure, we will recommend a doctor for anyone whose systolic pressure is above 130 mm Hg or whose diastolic pressure is above 80 mm Hg in a single test reading. State the null and alternative hypotheses.

 

(A) H0: systolic £ 130 and diastolic £ 80; Ha: systolic > 130 and diastolic > 80
(B) H0: systolic £ 130 and diastolic £ 80; Ha: systolic > 130 or diastolic > 80
(C) H0: systolic £ 130 or diastolic £ 80; Ha: systolic > 130 and diastolic > 80
(D) H0: systolic £ 130 or diastolic £ 80; Ha: systolic > 130 or diastolic > 80
(E) H0: systolic > 130 and diastolic > 80; Ha: systolic £ 130 or diastolic £ 80

 

 

13.

In #12, what would constitute Type I and Type II error, respectively?

 

(A) needless referral to a doctor, missed diagnosis
(B) missed diagnosis, needless referral to a doctor
(C) needless referral to a doctor, erroneous referral to a doctor for a not-very-sick patient
(D) needless referral to a doctor, not applicable since Type II error is impossible here
(E) missed diagnosis, erroneous lack of referral to a doctor

 

 

14.

We perform an Excel-based simulation of a complex industrial process that involves 52 steps. If any one of the steps fails, we call the simulated batch a “failure”; otherwise, it is a “success.” Which of the following is true as we summarize our findings of 5,000,000 simulated trials?

 

(A)
(B)
(C)

(D)
(E)

 

 

 

15.

Lung cancer among nonsmokers is rare. Let us assume that P(lung cancer | nonsmoker) = 0.0019 for the sake of this problem. If the probability of smoking is .22 and the probability of lung cancer given smoking is .18, compute the probability of lung cancer in the overall population.

 

(A) 0.036
(B) 0.038
(C) 0.039

(D) 0.040
(E) 0.041