3) In a presidential election year, candidates want to know how voters in various parts
of the country will vote. Suppose that 1 month before the election a random sample
of 540 registered voters from one geographic region is surveyed. From this sample
320 indicate that they plan to vote for this particular candidate. Based on this
survey data, find the 95% confidence interval estimate of this candidate’s current
support in this geographic area.
5) A company that receives shipments of batteries tests a random sample of nine of
them before agreeing to take a shipment. The company is concerned that the true
mean lifetime for all batteries in the shipment should be 50 hours. From experience
it is safe to conclude that the population distribution of lifetimes is normal with a
standard deviation of 3 hours. For one shipment the mean lifetime for a sample of
nine batteries was 48.2 hours. Test the hypothesis with = 0.01 level of
significance if the null hypothesis is that the population mean lifetime is 50 hours.
6) A wine producer claims that the proportion of its customers who cannot
distinguish its product from frozen grape juice is, at most, 0.09. The producer
decides to test this null hypothesis against the alternative that the true proportion
is more than 0.09. He asked randomly chosen 150 customers and 20 could not
distinguish its product from frozen grape juice. Test the hypothesis with = 0.005
level of significance.
7) The quality-control manager of a chemical company randomly sampled twenty 100-
pound bags of fertilizer to estimate the variance in the pounds of impurities. The sample variance was found to be 6.62. Find a 99% confidence interval for the population variance in the pounds of impurities.
8) An instructor has decided to introduce a greater component of independent study into an intermediate microeconomics course as a way of motivating students to work
independently and think more carefully about the course material. A colleague
cautions that a possible consequence may be increased variability in student
performance. However, the instructor responds that she would expect less variability.
From her records she found that in the past, student scores on the final exam for this
course followed a normal distribution with standard deviation of 18.2 points. For a classof 25 students using the new approach, the standard deviation of scores on the final exam was 15.3 points. If these 25 students can be viewed as a random sample of all those who might be subjected to the new approach, test the null hypothesis that the population standard deviation is at least 18.2 points against the alternative that it is lower
