Q1: The weights of packets of cookies produced by a manufacturer have a normal distribution with mean 202 grams and standard deviation 3 grams. What is the weight that should be written on the packet so that only 1 percent is underweight?
Q2: A company receives a very large shipment of components. A random sample of sixteen of these components is checked, and the shipment is accepted if fewer than two of the sampled components are defective. What is the probability of accepting a shipment containing 25% defectives?
Q3: You are interested in the proportion of smokers. Consider a population consisting of N = 4 elements: the first two persons smoke, while the remaining two do not smoke. That is {S, S, N, N}
(a) In this population, what is the proportion of smokers?
(b) You take a random sample of size n = 2. How many different random samples are possible?
(c) Write down the sampling distribution of P, the sample proportion of smokers in a random sample of size n = 2 from this population. That is, list the possible outcomes (sample proportions of smokers) and the associated probabilities.
(d) Calculate the mean of the sampling distribution.
Q4: 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.
Q5: 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.
Q6: 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.