###### BASICS OF TESTING HYPOTHESIS

###### NUMERICAL

Q. Calculate the variance and standard deviation for the following data-

Hemoglobin- 9.1-10(11), 10.1-11(14), 11.1-12(28), 12.1-13(22), 13.1-14(16), 14.1-15(12), 15.1-16(8)

Q. Calculate the mean for the following data-

Age in years- 1-6(6), 7-12(11), 13-18(25), 19-24(20), 25-30(15), 31-36(18)

Q. The following is the data on gain in body weight of two groups of young rats(28 to 30 days) maintained on two types of diet (high and low protein). Calculate whether the change in the body weight is observed due to diet or not using unpaired paired student t-test. (Critical value=1.83)

Q. Haemoglobin value (gm%) were estimated before and after the treatment with vitamin B12 in 06 human volunteers. Calculate whether the changes were significant due to drug therapy or not by applying paired t-test. (critical value at 5% level of significance = 2.571)

Q. Determine if there is any association between whooping cough and tonsillectomy in a random sample of 100 children in a school with the following data (critical value = 5.41 at P˂ 0.02)

Q. Find the mean, standard deviation and coefficient of variation for the following blood pressure measurements: 100,98,101,94,104,102,108,108.

Q. The following data for blood protein (gm/100ml) were observed for the comparison of two drugs, both drugs being tested on each person in random manner. Perform statistical test for drug differences at 5% level.

Q. It is hypothesized that the difference between two drugs with regard to success rate is zero (i.e. the two drugs are not different). What size sample is needed to show a difference of 20% significant at the 5% level with a β error of 10% ?(assume that the response rate is about 50% for both drugs & study is a two independent sample design.

Q. A tablet is produced with a labeled potency of 100mg. the standard deviation is known to be 10. What size sample should be assayed if we want to have 90% power to detect a difference of 3mg from the target? The test is done at 5% level.

Q. A parallel design is used to measure the effectiveness of a new anti-hypertensive drug with one group of patient receiving the drug and the other group receiving the placebo, a difference of 6mm Hg is considered to be of practical significance, the standard deviation is unknown but is estimated as 5 based on preliminary data. α is set at 5% & β at 10%. How many patients should be used in each group?

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