**Abhaya Indrayan**

**Biostatistics for Medical, Nursing and Pharmacy Students**

**Prentice-Hall of India, 2006**

**______________________________________________________________**

__Sample MCQs and other statistical exercises__**See the book for solutions**

1. What is statistical significance? How is it different from medical significance? Explain with the help of examples. (Extra credit for correct answer.)

2. Suppose the normal level of haemoglobin (Hb) in children is 13.6 g/dl. A study on a random sample of 10 children with chronic diarrhoea revealed that the mean is 12.8 g/dl and SD is 1.67 g/dl. The objective is to find that the Hb level in children with chronic diarrhoea, on average, have less than normal Hb level or not.

(i) State the null and alternative hypothesis.

(ii) What test criterion will you use to test the null hypothesis?

(iii) Carry out the statistical test.

(iv) Write your conclusion.

3. With the help of examples, contrast between

(i) null and alternative hypothesis.

(ii) Type I and Type II errors.

(iii)

*P*-value and level of significance.

(iv) Type II error and power.

4. What is statistical power? Where is this used? Give examples. (Extra credit for correct answer.)

5. Use court analogy to explain why a null hypothesis is either rejected or not rejected, but is never accepted.

6. With the help of examples, explain the difference between

(i) one-sample and two-sample

*t*-test.

(ii)

*t*-test and

*F*-test.

(iii) two-sample

*t*-test and paired

*t*-test.

(iv) one-sided and two-sided alternatives.

7. A randomized trial for comparing efficacy of two regimens showed that the difference is significant with

*P*<0.01. But in reality the two drugs do not differ in their efficacy. This is an example of

a. Type I error (alpha-error). b. Type II error (beta-error).

c. 1 – a. d. 1 – b.

8. A trial was conducted on 15 patients with a new drug and another 15 patients on placebo. The difference found is as much as 20 percent in the efficacy but it is not found statistically significant. This can happen due to all of the following except

a. high Type I error. b. small sample size.

c. lack of power. d. high Type II error.

9. Type I error is

a. accepting a null hypothesis. b. accepting a null hypothesis when false.

c. rejecting a null hypothesis. d. rejecting a null hypothesis when true.

10. Type II error is

a. not rejecting a null hypothesis. b. not rejecting a null hypothesis when false.

c. rejecting a null hypothesis. d. rejecting a null hypothesis when true.

11. What is statistical significance? How is it different from medical significance. Explain with the help of examples. (Extra credit for correct answer.)

12. A pharmaceutical company asserts that its new drug is definitely more effective than the existing drug in the market for controlling lipid levels. If you want to verify this claim, your null hypothesis would be

a. the new drug has more efficacy than the existing drug.

b. the new drug has same efficacy as the existing drug.

c. the new drug has less efficacy than the existing drug.

d. the new drug has no effect.

13.

*P*-value is the probability of

a. not rejecting a null hypothesis when true. b. rejecting a null hypothesis when false.

c. rejecting a null hypothesis when true. d. not rejecting a null hypothesis when false.

14. The probability of Type II error is called

a.

*P*-value. b. level of significance.

c. alpha. d. beta.

15. The probability of Type I error is called

a.

*P*-value. b. level of significance.

c. alpha. d. beta.

16. Statistical significance does not imply

a. that the probability of rejecting a true null hypothesis is small.

b. that

*P*-value is less than the level of significance a.

c. that the difference has arisen by chance.

d. that the difference is likely to persist from sample to sample.

17. True or false?

(i)

*P*-value can be more than the level of significance.

(ii) Type I error is more serious than Type II error.

(iii) Type II error is more serious than Type I error.

(iv) Power is 1 – a.

(v) Type II error and beta error are same.

(vi) b = 1 – a.

18. Consider the following data on body mass index (BMI) and forced vital capacity (FVC) in 12 persons:

Individual No. 1 2 3 4 5 6 7 8 9 10 11 12

BMI (kg/m2) 21 18 25 27 22 21 24 20 19 24 25 20

FVC (l) 3.5 2.7 4.2 3.9 3.1 2.8 3.7 4.1 3.0 3.8 3.1 3.7

Can you conclude that the mean FVC in those with BMI <25 kg/m2 is different from those with BMI >=25 kg/m2? Carry out an appropriate statistical test. State the null and the alternative hypothesis, the level of significance that you propose to use, and the conditions under which your test is valid.

19. A batch of 5 patients is given an exercise test to find if it raises the systolic level of blood pressure (sysBP) for at least one hour:

SysBP before the exercise 118 120 140 128 130

SysBP one hour after the exercise 127 128 132 136 130

Do these data acceptably support the hypothesis that the exercise raises average sysBP for at least one hour?

20. If sample mean is 3, the null hypothesis is µ = 0, sample standard deviation

*s*= 10, and the sample size

*n*= 100, then

a.

*z*= 0.3 b.

*t*= 0.3.

c.

*z*= 3. d.

*t*= 3.