Introductory Statistics Quiz 5

Math 140 Quiz 5 Name: __________________ 1. What is the purpose of statistical inference? To estimate or test an unknown population parameter using the statistic from the sample. 2. Verbal SAT scores of a sample of 300 students at a particular university had a mean of 592. According to the university's reports, verbal SAT scores of all its students had mean 580. Identify the population, the sample, the parameter, and the statistic: Population: All the students at the university Sample: The 300 students from the university Parameter: The mean SAT scores of all the students, which is 580. Statistic: The mean SAT scores of the students in the sample, which is 592. 3. True or False? If the statement is false, change some of the words to make it true. Consider a sampling distribution for the sample means. According to the Central Limit Theorem: T F the center of the sampling distribution is the population mean regardless of the sample size. T F the variability of the sampling distribution increases as the sample size increases. decreases T F the shape of the sampling distribution gets closer and closer to a normal distribution as the sample size increases. MORE ON THE NEXT PAGE! 4. Suppose random samples are taken in both California and Alaska in order to estimate the value of a certain population parameter for each state (for example, the proportion of the state’s residents that have a college degree). Which one of these samples is more likely to give an accurate estimate of its state’s population parameter? A random sample of a 1000 people from California, or a random sample of 1000 people from Alaska. a. The random sample of 1000 people from Alaska is more likely to give an accurate estimate of its state’s population parameter because the population of Alaska is smaller than the population of California. b. The random sample of 1000 people from California is more likely to give an accurate estimate of its state’s population parameter because the area of California is smaller than Alaska. c. Both random samples are equally likely to give an accurate estimate of their state’s population parameter because the population size doesn’t matter, only the size of the sample. 5. Fill in the blanks: a. The fact that different random samples from a population will give somewhat different results is called _______sampling variability_____________. b. The distribution of the sample statistic for all the possible SRSs of the same size from the same population is called _______sampling distribution______________ .