A pharmaceutical company is testing a new drug for side effects. One in eight pe

Question

A pharmaceutical company is testing a new drug for side effects. One in eight people tested experienced side effects. If the drug is administered to 10 people, find the probability that 3 people experience side effects. a) The contents of buttons in a carton is supposed to be less than or equal to 120 with a standard deviation 21. A lot of complaints have been received that the cartons are overfilled. A batch of l44 cartons was measured and found to have an average number of123 buttons. Prepare a hypothesis test to show that indeed the cartons may be overfilled. The probability of making a type 1 error was 0.01.Test whether the null hypothesis H_0: mu lessthanorequalto 120 should be accepted or rejected b) What is the p-VALUE for the test z value in a) above. c) If you are given the only the sample standard deviation (19) instead of the population standard deviation (21) test the hypothesis above H_0: mu lessthanorequalto 120

Explanation / Answer

Ho : Mean <= 120

Ha : Mean > 120

Significance limit (alpha) = 0.01

n ( sample size) = 144

Z statistic = (123 - 120) / SE

SE ( standard error ) = 21

Z- statistic = 3 / 21 = 0.143

Using standard normal distribution table

This is a one tail test

Probability ( < 0.143 ) [ p - value] = 0.0557 which is more than our acceptance limit so we cannot reject the null hypothesis

In case of sample std deviation = 19

SE = 19 / sqrt(144) and rest of the methodology is same

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