Question

1. Suppose a researcher, interested in obtaining an estimate of the average level of some enzyme in a certain human population, takes a sample of 36 individuals, determines the level of the enzyme in each, and computes a sample mean of 22. Suppose further it is known that the variable of interest is approximately normally distributed with standard deviation of 7. Give a 94% confidence interval of population mean.
2. Suppose we find that, the average engine size in our sample of size n = 30 is 192 cubic inches, with a standard deviation of 104 cubic inches. Use these statistics to compute a 90% confidence interval of population mean, that is, the average engine size for all.
3. Suppose the Dean of our college claims that, the average GPA for all students in the college is at least 3.00, with standard deviation 0.4. However, from a class with 25 students, we find the class average GPA is 2.80. Can we reject the dean’s claim at significance level 0.05? (We conduct a hypothesis testing).

4. a). H0: mu=3.00,          Ha:

   b). Calculate test statistic, here is z-value.

   c). Find pvalue

   d). Make your decision.

Answer 1