Download Elementary Statistics Exam 3: Confidence Intervals and Hypothesis Testing - Prof. Kane Nas and more Exams Statistics in PDF only on Docsity! Math 220 : Elementary Statistics Kane Nashimoto Exam 3 - Ch. 6, 7, 8 Spring 2008 Name : Directions: This exam contains five problems worth a total of 100 points. For each computa- tional problem, you must first write the formula to be used and present all your subsequent work in order to receive full or partial credit. Circle your final answers. 1. A box of paperclips manufactured by a certain company says, “Contains approxi- mately 100 paperclips.” A high school student wanted to estimate the mean number of paperclips contained in the box. He selected a random sample of 20 boxes and counted the actual numbers of paperclips. He observed a sample mean of 103.10 with a standard deviation of 2.02. Assume that the number of paperclips can be characterized as having a normal distribution. (a) Form a 95% confidence interval for the true mean number of paperclips contained in the box. (12 pts.) (b) Based on your answer in (a), can you conclude that the true mean number of paperclips contained in the box is greater than 100? Explain. (10 pts.) (c) If the student wants to be 95% sure that his estimate of the mean number of paperclips is off of the true value by no more than 0.5, how many boxes should he observe? (10 pts.) 1 2. The administrators of a college claim that less than 30% of their students are regular smokers. According to a survey conducted with a random sample of 250 students at this college, 72 of them stated that they were regular smokers. Test the truth of the claim at a significance level of .01. (14 pts.) H0 : vs. Ha : Compute the test statistic and calculate the p-value. Should the null hypothesis be rejected? Circle one. Yes No 3. As part of the routine quality control, a company who manufactures athletic socks took a random sample of 750 pairs of socks for inspection from its production line. The company discovered that, of the 750 pairs, 18 were defective. (a) Construct a 90% confidence interval for the true proportion of defective pairs of socks. (12 pts.) (b) If the company wishes its estimate of the proportion of defective pairs of socks to be within .01 of the true value with 95% certainty, how many pairs of socks should the company inspect? (10 pts.) 2
