Question

A pharmaceutical company wants to answer the question of whether it takes longer than 45 seconds for a drug in pill form to dissolve in the gastric juices of the stomach. A sample was taken from patients taken the given drug in pill form and times for the pills to be dissolved were measured as the following

42.7 , 43.7 , 44.6 , 45.1 , 45.6 , 45.9, 46.8 , 47.6

A. State the hypotheses to test this question

B. State the Assumption of the test.

C. Perform the test and determine if it's statistically significant at a=0.05

D. Interpret the result.

Answer 1

Here, we have to use one sample t test for the population mean.

Part A

The null and alternative hypotheses are given as below:

H0: µ = 45 versus Ha: µ > 45

This is an upper tailed test.

Part B

We assume that the sample data is from normally distributed population.

Part C

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 45

Xbar = 45.25

S = 1.595529469

n = 8

df = n – 1 = 7

α = 0.05

Critical value = 1.8946

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (45.25 – 45)/[ 1.595529469/sqrt(8)]

t = 0.4432

P-value = 0.3355

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

Part D

There is not sufficient evidence to conclude that it takes longer than 45 seconds for a drug in pill form to dissolve in the gastric juices of the stomach.