Percentage investment in new-product development is monitored for a pharmaceutical company by quarter. The observations are listed row wise:
|
32.9
|
31.5
|
34.3
|
36.8
|
35.0
|
|
29.4
|
33.2
|
37.8
|
35.0
|
32.7
|
|
28.5
|
30.4
|
32.6
|
31.5
|
30.6
|
|
35.8
|
36.4
|
34.2
|
35.0
|
33.5
|
|
31.8
|
32.5
|
28.4
|
33.8
|
35.1 |
|
30.2
|
33.0
|
34.6
|
32.4
|
32.0
|
(a) Can we conclude that the sequence of investment percentages is random? Use α= 0.05.
(b) Is there clustering? Is there a trend? Use α = 0.05.
(c) Can you conclude that the distribution of investment percentages is normal? Use α= 0.01.
(d) Find a 98% confidence interval for the mean percentage investment.
(e) Find a 98% confidence interval for the standard deviation of the percentage investment.
(f) Can we conclude that the mean percentage investment in new products exceeds 31%? Use α = 0.01. What is the p-value? Explain.