Please solve following questions

Q#1

(a)A random sample of boots worn by 40 combat soldiers in a desert region showed an average life of 1.8 years with a standard deviation of 0.05. Under the standard conditions, the boots are known to have an average life of 1.28 years. Is there reason to assert at a level of significance of 0.05 that use in the desert causes the mean life of such boots to decrease?

(b b) An auditor for an insurance company would like to determine the proportion of claims selected by the company within 2 months of the receipt of the claim. A random sample of 200 claims is selected, and it is determined that 80 were paid the money within 2 months of the receipt of the claim. Setup a 99 per cent confidence interval estimate of the population proportion of the claims paid within 2 months.

Q#2.

To test the desirability of a certain modification in typist’s 9 typists were given two tests of almost same nature, one n the desk in use and the other on new type. The following difference in the number of words typed per minute was recorded:

Typist

A

B

C

D

E

F

G

H

I

Increase in No. of words

2

4

0

3

-1

4

-3

2

5

Do the data indicate that the modification in desk increases typing speed?