Question

Company officials are concerned about the length of time a particular drug retains its
potency. A random sample of 9 bottles of the product is drawn from current production
and each bottle divided in half. One half was analyzed for potency. The other half was
stored for one year, and then analyzed. The readings obtained are as follows. Higher
numbers indicate higher potency. Is the mean potency the same after one year?
Test at the .05 level of significance.
Bottle	A	B	C	D	E	F	G	H	I
Current Output	10.2	10.7	10.3	10.2	9.8	10.6	10.4	9.8	10.2
Stored Samples	10.1	10.5	10.1	9.8	9.6	10.5	10.3	9.6	10.3

The mean potency (is / is not) the same after one year.

Answer 1

H0: Null Hypothesis: ( the mean potency is the same after one year) (Claim)

HA: Alternative Hypothesis: ( the mean potency is not the same after one year)

From the data, the following statistics are calculated:

n1 = 9

1 = 10.2444

s1 = 0.3087

n2 = 9

2 = 10.0889

s2 = 0.3516

Pooled standard deviation is given by:

The Test Statistic is given by:

= 0.05

ndf = n1 + n2 - 2 = 9 + 9 - 2 = 16

From Table, critical values of t = 2.1199

Since the calculated value of t = 0.0092 is less than critical value of t = 2.1199, the difference is not significant. Fail to reject null hypothesis.

Correct option:

The mean potency is the same after one year.