1: The average fill volume from a random sample of 49 bottles of an energy drink is 32.8 ounces; the standard deviation among the individual fill volumes is3.5 ounces. Determine a 95 percent confidence interval for the mean fill weight.
2: Continuation of previous problem. Determine the probability value for testing the research hypothesis that the mean fill volume is less than 33 ounces. Use the sample information in the previous problem and state your conclusion assuming a significance level of 5 percent.
3: We are interested in the proportion of UoI students who smoke. A random sample of n = 400 UoI students is taken. The proportion of smokers in this random sample is 0.25.
Calculate a 95 percent confidence interval for the unknown proportion of smokers among the UoI student population.
4: Consider the following regression model:
Salary(in $ 1000) = 20 + (2)X + (5)Z + (0.7)(X*Z)
where X is the number of years of experience, and Z is an indicator variable that is 1 if you have obtained an MBA degree and 0 otherwise; X*Z is the product between years of experience and the indicator variable Z.
Graph salary (Y) against years of experience (X). Do this for both groups (without MBA, with MBA) on the same graph.
Does experience matter? Is it worth getting an MBA? Interpret the graph.
5: The temperature in Jihlava follows a normal distribution with mean 50 degrees and standard deviation 10 degrees. You select one day at random. What is the probability that at that day the temperature will be above 60?
6: A consignment of twelve electronic components contains one component that is faulty. Two components are chosen randomly from this consignment for testing. What is the probability that the faulty component will be one of the two components chosen for testing?