Statistics 2 ( Please give me solutions step by step)

Problem 1

The article "n-Nonane Hydro-conversion on Ni and Pi Containing HMFL, HMOR and HBEA" ( G. Kinger and H. Vinck, Applied Catalysis A : General, 2002: 139-149) presents hydro-

conversion rates (in . ) of n-nonane over both HMFI and HBEA catalysis. The results are as

follows: HMFL: 0.43 0.93 1.91 2.56. 3.72 6.19 11.00 HBEA: 0.73 1.12 1.24 2.93

(a) Can you conclude that the mean rate differs between the two catalysis?

Problem 2

A random number generator is supposed to produce the digits 0 through 9 with equal probability. A sample of 200 digits was generated, with the following frequency for each of the digits.

Digit 0 1 2 3 4 5 6 7 8 9

Frequency 21 17 20 18 25 16 28 19 22 14

(a) Do these data provide evidence that the random number generator is not working properly? Show your full work and explain.

Problem 3

One of the factors that determines the degree of risk a pesticide poses to human health is the rate at which the pesticide is absorbed into skin after contact. An important question is whether the amount in the skin continues to increase with the length of the contact, or whether it increases for only a short time before leveling off. To investigate this, measured amounts of a certain pesticide were applied to 20 samples of rat skin. Four skins were analysed at each of the time intervals 1, 2, 4, 10 and 24 hours. The

amounts of the chemical (in ) that were in the skin are given to the following table.

Duration. Amount Absorbed

1 1.7 1.5 1.2 1.5

2 1.8 1.6 1.8 1.9

4 1.9 1.7 2.1 2

10 2.3 1.9 1.7 1.5

24 2.1 2.2 2.5 2.3

(a) Construct an ANOVA table. You may give a range for the p-value.

(b) Can you conclude that the amount in the skin varies with time?