Question

4. In order to test whether brand-name printer cartridges produce more printed pages, on average, than generic cartridges, a research firm has 6 randomly selected printer users use both types of cartridges and record how many pages were printed with each. The number of pages printed for each user by each type of cartridge are shown on the answers sheet in cells F92 to G98.

Use the 0.01 significance level to test whether the brand-name cartridges print more pages on average than the generic cartridges.

Identify and interpret the p-value for the test.

DATA:

User	Name Brand	Generic
1	306	300
2	256	260
3	402	357
4	299	286
5	306	290
6	257	260

ANSWERS MUST FOLLOW THIS FORMAT:

Define H0 :
Define H1 :
Test statistic
Critical value of test statistic
Decision rule
Calculated value of test statistic
Reject or fail to reject H0?
Conclusion about the cartridges
Find the p-value
Interpret p-value

Answer 1

(1)

H0: Null Hypothesis:

(2)

HA: Alternative Hypothesis:

(3)

From the given data, the following statistics are calculated:

n1 = 6

1 = 304.33

s1 = 53.20

n2 = 6

2 = 292.17

s2 = 35.71

Test statistic is:

t = (304.33-292.17)/26.158 = 0.4649

So,

Test statistic is:

0.4649

(4)

= 0.01

ndf = n1 +n2 - 2 = 6 + 6 - 2 = 10

One Tail - Right Side

From Table, critical value of t= 2.7638

So,

Critical value of test statistic = 2.7638

(5)

Since calculated value of t is less than critical value of t:

Fail to reject H0.

(6)

Conclusion:

The data do not support the claim that brand - name printer cartridges produce more printed pages, on average, than generic cartridges.

(7)

By Technology, P- Value = 0.3260

(8)

Since P - Value is greater than , the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that brand - name printer cartridges produce more printed pages, on average, than generic cartridges.