Develop the Likelihood Ratio Test to test Ho: H= 10 vs Ha: 10 when sampling from a normal distribution with variance equal to 16. Assume n = 4, x= 0.10

Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with s.d.= 2.3% . A random sample of 12 Australian bank stocks has a sample mean of x=6.16% . For the entire Australian stock market, the mean dividend yield is 7.2%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 7.2%? Find (or estimate) the P-value. Round your answer to three decimal places.

Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with  mean 2.65 and standard deviation 0.85.   If a random sample of 25 specimens is selected, what would be the standard error of the mean?

The shelf life of a perishable product is a random variable that is related to customer acceptance and, ultimately, to sales and profit. Suppose the shelf life of a particular soft drink is best approximated by a normal distribution with a mean of 180 days and standard deviation 20 days. What fraction of the product will still be fresh after 5 months on the shelf?