1. A nutritionist created a 99% confidence interval to estimate the average amount of salt (grams) consumed by an individual per day to be (5.4, 9.5) grams. What is the value of the margin of error of this confidence interval?

Please give your answer correctly rounded to two decimal places and do NOT include units in your answer.

2. An electricity provider wants to estimate the mean time it takes for customers to get an electrical fault resolved. The provider took a random sample of 36 customers who had recently reported an electrical fault and found a mean time of 11.07 hours. Assume the population standard deviation is 0.79 hours. What is the value of the width for a 95% confidence interval?

Please give your answer correctly rounded to two decimal places. (Do NOT give units.)

3. The production manager at a textile mill, believes that a new machine, producing cloth, is not working according to the company's specifications. A sample of 78 pieces of cloth reveals a sample mean breaking strength of 40.8 Kg and a standard deviation of 0.2 Kg. The company requires that the cloth should have a mean breaking strength of 45 Kg. The manager wants to do a hypothesis test of the mean. What value of the mean would be used in the null and alternative hypotheses?

4. Production managers on an assembly line must monitor output to check the average weight (kilograms) of their product. If the average weight is less than 15 kilograms, the assembly line must be stopped, and the machinery serviced. They continuously inspect a random sample of production runs and find the average weight of a sample of products, to check that the manufacturing process is working correctly. The hypotheses are:

Ho: = 15

Ha: < 15

Say a random sample of 30 products is taken, where the mean weight is found to be 5.4 kilograms with a standard deviation of 0.4 kilograms. If testing at the 1% level of significance, what is the critical value?

Please give your answer correctly rounded to two decimal places.