Study Questions Ch 8

Study Questions Ch 8 1) When all the items in a population have an equal chance of being selected for a sample, the process is called _________________. A. Simple random sampling B. z-score C. Sampling error D. Nonprobability sampling 2) What is the difference between a sample mean and the population mean called? A. Standard error of the mean B. Sampling error C. Interval estimate D. Point estimate 3) Suppose we select every fifth invoice in a file. What type of sampling is this? A. Random B. Cluster C. Stratified D. Systematic 4) All possible samples of size n are selected from a population and the mean of each sample is determined. What is the mean of the sample means? A. The population mean B. Larger than the population mean C. Smaller than the population mean D. Cannot be estimated in advance 5) When dividing a population into subgroups so that a random sample from each subgroup can be collected, what type of sampling is used? A. Simple random sampling B. Systematic sampling C. Stratified random sampling D. Cluster sampling 6) As the size of the sample increases, what happens to the shape of the distribution of sample means? A. Cannot be predicted in advance. B. Approaches a normal distribution. C. Positively skewed. D. Negatively skewed. 7) The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. Based on a large number of observations, the distribution of trout weights is normally distributed with a mean of 402.7 grams and a standard deviation 8.8 grams. What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams? Z X  / n 405.5 402.7 8.8 / 40 2.8 8.8 / 6.325 2.01 from the Z-table p = 0.4778 P(X > 405.5) = 0.5 – 0.4778 = 0.0222 8) Suppose a research firm conducted a survey to determine the average amount of money steady smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample mean is $20 and the sample standard deviation is $5. What is the probability that a sample of 100 steady smokers spend between $19 and $21? Z X  / n 19 20 5 / 100 1 5 / 10 2.0 from the Z-table p = 0.4772 Z X  / n 21 20 5 / 100 1 5 / 10 2.0 from the Z-table p = 0.4772 P(19< X < 21) = 0.4772 + 0.4772 = 0.9544 10) The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard deviation of the sample of 4.2 tons. What is probability that a truck will weigh less than 14.3 tons? Z X  / n 14.3 15.8 4.2 / 49 1.5 0.6 P(X< 14.3) = 0.5 – 0.4938 = 0.0062 2.5 from the Z-table p = 0.4938