Find the following for the below situations:

1: Null and Alternative Hypotheses

2: Test Statistic

3: The probability you would calculate for the P-Value in the following:

A) From past records 30% of a company's orders come from new customers. The firm has recently mounted a publicity campaign to attract new customers. To test the efficacy of this it agrees to take the next 20 orders as a sample.

B) When a Car wash is working properly each wash takes a mean of 2 minutes 30 seconds and the duration is normally distributed. When it is faulty it takes longer on average. The proprietor tests the machine at the start of each week by running it 5 times.

1) An electrical firm manufactures light bulbs that have a lifetime, which is normally distributed. A sample of 30 bulbs has an average life of 788 and a standard deviation of 40. Test H0: M=800 against H1: M < 800. Use significance level of 0.04

Suppose in questions 1 that the alternative hypotheses were H1: M canâ€™t not equal 800. How would this affect the p-value? What is the conclusion of the test now?

2) A production process gives components whose strengths are normally distributed with a mean of 40lbs and unknown variance. The process is modified and 12 components are selected at random giving strengths:

39.8 40.3 43.1 39.6 41.0 39.9 42.1 40.7 41.6 42.1 40.8 42.5

Is there any evidence that the modified process gives stronger components?

**Subject Mathematics Advanced Statistics**