Question

6.3.7 A manufacturer wants to assess whether or not rods are being constructed appro- priately, where the diameter of the rods is supposed to be 1.0 cm and the variation in the diameters is known to be distributed Nu, 0.1). The manufacturer is willing to tolerate a deviation of the population mean from this value of no more than 0.1 cm, i.e., if the population mean is within the interval 1.0 +0.1 cm, then the manufacturing process is performing correctly. A sample of n = 500 rods is taken, and the average diameter of these rods is found to be i = 1.05 cm, with s? = 0.083 cm. Are these results statistically significant? Are the results practically significant? Justify your answers. 6.3.8 A polling firm conducts a poll to determine what proportion of voters in a given vote in an upcoming election. A random sample of n = 250 was taken from the population, and the proportion answering yes was 0.62. Assess the hypothesis Ho : 0 = 0.65 and construct an approximate 0.90-confidence interval for 0. 6.3.9 A coin was tossed n = 1000 times, and the proportion of heads observed was 0.51. Do we have evidence to conclude that the coin is unfair? 6.3.10 How many times must we toss a coin to ensure that a 0.95-confidence interval for the probability of heads on a single toss has length less than 0.1, 0.05, and 0.01, respectively? 6.3.11 Suppose a possibly biased die is rolled 30 times and that the face containing two pips comes up 10 times. Do we have evidence to conclude that the die is biased? 6.3.12 Suppose a measurement on a population is assumed to be distributed N (1,2) where u ER is unknown and that the size of the population is very large. A researcher wants to determine a 0.95-confidence interval for that is no longer than 1. What is the minimum sample size that will guarantee this?

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