# Biostatistics Homework

1. US Census statistics show that college graduates make more than $254,000 more intheir lifetime than non-college graduates. If you were to question the validity ofthis observation, what would be your basis for doing so?

A. Definition of a college graduate

B. Work lifestyles of the population

C. Defining â€œlifetimeâ€

D. How the Census was taken

2. The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

A. must be more than 22, since the population is always larger than the sample

B. must be less than 22, since the sample is only a part of the population

C. could not be 22

D. could be larger, smaller, or equal to 22

3. Since a sample is a subset of the population, the sample mean

A. is always smaller than the mean of the population

B. is always larger than the mean of the population

C. must be equal to the mean of the population

D. can be larger, smaller, or equal to the mean of the population

Use the following situation for Questions 4-7. Michael, Inc., a manufacturer ofelectric defibrillators, is a firm that makes 50 types of electric defibrillators . Thetable below shows the price distribution of the defibrillators .

Price (In $) Number of Defibrillators

100 â€“ 130 8

140 – 170 12

180 – 210 20

220 – 250 10

TOTAL 761.22

Select from the following choices for Questions 4-7. Use letter only in the blank.

A. 32 B. 50% C. 20 D. 30 E. 16% F. 10 G. 60% H. 50

4. How many defibrillators have a price of at least $180?__ D. _____

5. What percentage of the defibrillators has a price of at least $180? ___%___

6. What percentage of the defibrillators has a price of less than $140? ___ E. __

7. How many defibrillators cost at least $140 but no more than $210? __ A. ____

8. Temperature is an example ofa quantitative variable

A. a qualitative variable

B. a quantitative variable

C. either a quantitative or qualitative variable

D. neither a quantitative nor qualitative variable

Use the following situation for Questions 9 and 10.

The following frequency distribution shows the frequency of outbreaks of theï³1ï¡1 virus (statistics flu) for the following households in a small rural community.

Households 1134 406 168 41 25 12 : 1786

Outbreaks 0 1 2 3 4 5

9.

Use the frequency distribution to construct a probability distribution by filling in

the blanks below.

x 0 1 2 3 4 5

P(x) P(0) = P(1) = P(2) = P(3) = P(4) = P(5) =

10. Compute the mean and the standard deviation and select from the following the appropriate interpretation of the results (select best response)

A. A household on the average has 0.9 outbreaks with a standard deviation of.6 outbreaks

B. A household on the average has 0.6 outbreaks with a standard deviation of12 outbreaks

C. A household on the average has 0.9 outbreaks with a standard deviation of.9 outbreaks

D. A household on the average has 0.6 outbreaks with a standard deviation of.9 outbreaks

Use the following situation for Questions 11 – 13.

Twenty students were randomly selected for cholesterol screening. The following

data were collected.

260 164 210 225 244 254 233 184 269 206

158 209 221 213 198 179 214 257 246 221

11. Using the information above compute the following: (Round to nearest hundredth)

A. Mean = _____

B. Median = _____

C. Mode = _____

D. Sample Standard Deviation = _____

E. The Sample Variance = ______

F. The Coefficient of Variation = ______ (as a percent, for example 27.43%)

12. Is the data skewed _______ (select correct letter from list below)

A. No B. Skewed left C. Skewed right D. Unable to determine

13. Which is the best measure of central tendency for the randomly selected cholesterol

screenings? _______ (select correct letter from list below)

A. Mean B. Median C. Mode D. It does not matter, one is as good as the other

14. Let event A = a patient does not survive a new treatment procedure for prostrate cancer and event B = the patient is permanently rendered sexually dysfunctional by

the new treatment. Furthermore, events A and B are mutually exclusive. Which of

the following statements is also true?

A. A and B are also independent. B. P(A or B) = P(A)P(B)

C. P(A or B) = P(A) + P(B) D. P(A and B) = P(A) + P(B)

15. Twenty-five percent of the employees of a large hospital are minorities. A random sample of 7 employees is selected.

A. What is the probability that the sample contains exactly 4 minorities? G. 0.0577

B. What is the probability that the sample contains fewer than 2 minorities? C. 0.4449

C. What is the probability that the sample contains exactly 1 non-minority? F. 1.3125

D. What is the expected number of minorities in the sample? I. 1.75

E. What is the variance of the minorities? F. 1.3125

Select from the answers below. Place the correct letter in the blanks above.

A. 0.5551 B. 1.1456 C. 0.4449 D. 0.0013 E. 1.7226

F. 1.3125 G. 0.0577 H. .0001 I. 1.75 J. 0.0286

16. The life expectancy of a lung cancer patient treated with a new drug is normally distributed with a mean of 4 years and a standard deviation of 10 months. (0.833)

A. What is the probability that a randomly selected lung cancer patient will last more than 5 years? B. 11.51%

B. What percentage of lung cancer patients will last between 5 and 6 years? A. 10.69% ____

C. What percentage of lung cancer patients will last less than 4 years? I. 50%

D. What percentage of lung cancer patients will last between 2.5 and 4.5 years?83.98 %

E. If the drug manufacturer guarantees the drug will be effective for a minimum of 3years (and will pay for the entire treatment program if the patient does not survive), what percentage of lung cancer patients will have to pay for the treatment? B. 11.51%

Select from the answers below. Place the correct letter in the blanks above.

A. 10.69% B. 11.51% C. .0796 D. 46.01% E. 88.49%

F. 68.9% G. 53.98% H. 0% I. 50% J. 0.06172

17. The life expectancy in the United States is 75 with a standard deviation of 7 years.

A random sample of 49 individuals is selected.

A. What is the standard error of the mean? C. 1.0

B. What is the probability that the sample mean will be larger than 77 years? F0.0228

C. What is the probability that the sample mean will be less than 72.7 years? A. 0.0107

D. What is the probability that the sample mean will be between 73.5 and 76 years? B. 0.7745

E. What is the probability that the sample mean will be between 72 and 74 years? J. 0.1573____

F. What is the probability that the sample mean will be larger than 73.46 years? H. 0.9389

Select from the answers below. Place the correct letter in the blanks above.

A. 0.0107 B. 0.7745 C. 1.0 D. 0.8427 E. 0.9772

F. 0.0228 G. 1/7 H. 0.9389 I. 22.55% J. 0.1573

18. The standard hemoglobin reading for healthy adult men is 15 g/110 ml with a standard deviation of ï³ï€ = 2 g. For a group of men, we find a mean hemoglobin of 16.0 g.

A. Obtain a 95% confidence interval for if the group size was 25

The calculation is as follows

16Â± 1.96 * 2/âˆš25 = (15.216, 16.784)

B. Obtain a 95% confidence interval for if the group size was 36__

B. 15.347 – 16.653 ___

C. Obtain a 95% confidence interval for if the group size was 49

A. 15.440 – 16.560

Select from the answers below. Place the correct letter in the blanks above.

A. 15.440 – 16.560 B. 15.347 – 16.653 C. 14.440 – 15.560

D. 14.316 – 15.684 E. 15.316â€“ 16.684 F. 14.347 – 15.653

19. Doubling the size of the sample will

A. reduce the standard error of the mean to one-half its current value

B. reduce the standard error of the mean to approximately 70% of its current value

C. have no effect on the standard error of the mean

D. double the standard error of the mean

20. The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large is based on the

A. central limit theorem

B. fact that we have tables of areas for the normal distribution

C. assumption that the population has a normal distribution

D. None of these alternatives is correct.

Use the following situation for Questions 21 – 23. In order to estimate the average time spent on the dialysis machines per kidney patient at a local university hospital, data were collected for a sample of 81 patients over a one week period.

Assume the population standard deviation is 1.2 hours.

21. The standard error of the mean is

A. 7.5 B. 0.014 C. 0.160 D. 0.133

22. With a 0.95 probability, the margin of error is approximately

A. 0.26B. 1.96 C. 0.21 D. 1.64

23. If the sample mean is 9 hours, then the 95% confidence interval is

A. 7.04 to 110.96 hours B. 7.36 to 10.64 hours

C. 7.80 to 10.20 hours D. 8.74 to 9.26 hours

24. The t distribution is applicable whenever:

A. the sample is considered large (n ï‚³ï€ 30).

B. the population is normal and the sample standard deviation is used toestimate the population standard deviation

C. n ï‚³ï€ 100

D. n ï‚³ï€ 1000

Use the following situation for Questions 25 â€“ 26.

A random sample of 16statistics examinations from a large population was taken. The average score inthe sample was 78.6 with a variance of 64. We are interested in determiningwhether the average grade of the population is significantly more than 75. Assume

the distribution of the population of grades is normal.

25. The test statistic is: A. 0.45 B. 1.80 C. 3.6 D. 8

26. At 95% confidence, it can be concluded that the average grade of the population

A. is not significantly greater than 75

B. is significantly greater than 75

C. is not significantly greater than 78.6

D. is significantly greater than 78.6

27. Independent samples are obtained from two normal populations with equalvariances in order to construct a confidence interval estimate for the differencebetween the population means. If the first sample contains 16 items and the secondsample contains 36 items, the correct form to use for the sampling distribution isthe

A. normal distribution

B. t distribution with 15 degrees of freedom

C. t distribution with 35 degrees of freedom

D. t distribution with 50 degrees of freedom

Use the following situation for Questions 28 â€“ 33. A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You

are given the following results.

Today Five Years Ago

Mean 82 88

Variance 112.5 54

Sample Size 45 36

28. The difference between the means of the two populations is (d) =

A. 58.5 B. 9 C. -9 D. -6

29. The standard deviation of the difference between the means of the two populations is

A. 12.9 B. 9.3 C. 4 D. 2

30. The 95% confidence interval for the difference between the two population means is

A. -9.92 to -2.08

B. -3.92 to 3.92

C. -13.84 to 1.84

D. -24.228 to 12.23

31. The test statistic for the difference between the two population means is

A. -.47 B. -.65 C. -1.5 D. -3

32. The p-value for the difference between the two population means is

A. .0014 B. .0028 C. .4986 D. .9972

33. What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.)

A. There is a statistically significant difference in the average final

examination scores between the two classes.

B. There is no statistically significant difference in the average final

examination scores between the two classes.

C. It is impossible to make a decision on the basis of the information given.

D. There is a difference, but it is not significant.

Use the following situation for Questions 34 â€“ 38. The director of a regional hospital is interested in determining whether or not the proportion of incoming female patients who needs a pap-smear has increased. A sample of female patients taken several years ago is compared with a sample of female patients this year.

Results are summarized below.

Sample Size No. Requiring Pap-Smear

Previous Sample 250 50

Present Sample 300 69

34. The difference between the two proportions is:

A. 50 B. 19 C. 0.50 D. – 0.03

35. The pooled proportion has a value of

A. 0.216 B. – 0.216 C. 1.645 D. 0.5

36. The interest of the director represents a

A. one tailed test

B. two tailed test

C. one tailed or a two tailed test, depending on the confidence coefficient

D. one tailed or a two tailed test, depending on the level of significance

37. The test statistics for this test is

A. 1.645 B. 1.96 C. 0.035 D. – 0.851

38. If the test is to be done with an ï¡ï€ =.05 the

A. null hypothesis should be rejected

B. null hypothesis should not be rejected

C. alternative hypothesis should be accepted

D. None of these alternatives is correct.

39. Regression analysis was applied between demand for a product (Y) and the price of the product (X), and the following estimated regression equation was obtained.

_Y

= 120 – 10 X

Based on the above estimated regression equation, if price is increased by 2 units,

then demand is expected to

A. increase by 120 units B. increase by 100 units

C. increase by 20 units D. decease by 20 units

40. If there is a very strong correlation between two variables, then the coefficient of correlation must be

A. much larger than 1, if the correlation is positive

B. much smaller than 1, if the correlation is negative

C. much larger than one

D. None of these alternatives is correct.

41. Regression analysis was applied between sales (in $1000) and advertising (in $100)

and the following regression function was obtained. _Y = 500 + 4 X

Based on the above estimated regression line if advertising is $10,000, then the

point estimate for sales (in dollars) is

A. $900 B. $900,000 C. $40,500 D. $505,000

Use the following situation for Questions 42 â€“ 46. You are given the following

information about y and x.

y x

Dependent Variable Independent Variable

5 15

7 12

9 10

11 7

42. The least squares estimate of b1 equals

A. -0.7647 B. -0.13 C. 21.4 D. 16.412

43. The least squares estimate of b0 equals

A. -0.7647 B. -1.3 C. 164.1176 D. 16.41176

44. The sample correlation coefficient equals

A. -86.667 B. -0.99705 C. 0.9941 D. 0.99705

45. The coefficient of determination equals

A. -0.99705 B. -0.9941 C. 0.9941 D. 0.99705

46. A researcher selected a sample of 50 residents from each of three different cities to determine if they were willing to participate in a medical experiment. At _ = .05, test the claim that the proportions who will participate are equal.

Residents City 1 City 2 City 3

Willing to participate 20 12 22

Not willing to participate 30 38 28

Total 50 50 50

A. There is not evidence to reject the claim that the proportions are equal because the test value 4.861 < 5.991

B. There is evidence to reject the claim that the proportions are equal because the test value > 1.042

C. There is not evidence to reject the claim that the proportions are equal because the test value 5.991< 12.592

D. There is evidence to reject the claim that the proportions are equal because the test value 5.991 > 1.042

47. A researcher is comparing samples from 6 different populations. Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 6 population means are not all equal. How many of the population means would be significantly different from the others?

A. Three (half) B. At least 1

C. All would be different D. More than 2

Use the following situation for Questions 48 â€“ 50. A research firm reported that15% of those surveyed described their health as poor, 26% as good, 40% as verygood, and 19% as excellent. A health professional in Chicago wanted to determine if people in Chicago had similar feelings toward their health. In a sample of 600 people in Chicago, 70 described their health as poor, 180 as good, 210 as very

good, and 140 as excellent. Complete the chart below by filling in the observed and expected values.

48.

observed expected

poor 70 90

good 180 156

Very good 210 240

excellent 140 114

Observed Expected

Poor

Good

Very Good

Excellent

49. Calculate the test statistic ________ (to two decimal places, i.e 2.34)

50. Given an ï¡ï€ = .05, what is the result of the chi-squared test?

A. There is not evidence to reject the claim that the proportions are equal because the test value is less than the critical ï£2 value.

B. There is evidence to reject the claim that the proportions are equal because the test value is greater than the critical ï£2 value.

C. There is not evidence to reject the claim that the proportions are equal because the test value is greater than the critical ï£2 value.

D. There is evidence to reject the claim that the proportions are equal because he test value is less than the critical ï£2 value.