• a) Under Australian and New Zealand food standards, a sausage can have no more than 500grams of fat per kilo of sausage. Ken's Super Sausages have a mean fat content of 490 grams per kilo, with a standard deviation of 4 grams.

1. What proportionof Ken's Super Sausages meet the standard, andwhat assumptiondid you need to make to determine this.

A random sample of 36 of Sam's Spicy Sausages had a mean of 495 grams of fat per kilo, and a standard deviation of 6 grams. We want to determine a 95% confidence interval for the fat content of Sam's Spicy Sausages:

1. Determinethe standard error

1. Determinethe critical value of t.

1. Thusfind the 95% confidence intervalfor mean fat level.

• b) A construction company buys bags of cement, which are supposed to have an average weight of 10kg. They suspect that their supplier is under filling the bags, but they don't want to accuse them unless they have strong evidence. They weigh a random sample of 25 bags without replacement from the most recent shipment of 250 bags, and find a mean weight of 9.80 kg and a standard deviation of 0.40 kg. They want to test at significance level of 1%.

1. Explainwhich one of the following is the appropriate pair of hypotheses for this situation.

1. Identifythe assumption that you need to make in order to perform the requested test.

1. Determinethe critical value(s)

1. Determinethe value of the standard error

1. Determinethe value of the test statistic

1. What is yourdecision?

1. What is yourconclusion?

• c) Your cosmetics company has just developed a new shampoo especially for red heads, and needs to know how large the potential market might be. Hairdressers tell you that they think the portion of the population with red hair is about 5%, but you need a more reliable estimate to dimension your market.Determinehow many people you would need to sample in order to be 95% confident of estimating the true (population) proportion of red heads within an error of 0.5%.