1a)

Which of the following statements about the sampling distribution of the mean [distribution of sample means] and the central limit theorem {BLT} are true? Select four [4} true statements from the list below: o I] . If pi = ,u. and of = , then the distribution of sample means is normal. \"I, II] . If the population is approximately normally distributed, then sample size does not matter for the central limit theorem to apply. I] . The shape of the sampling distribution is closer to the population shape as the sample size increases. II] . If a population is perfectly normal, then for the distribution of sample means of any size, pi = p and oi = o: II] . From the same population, the standard error of the sampling distribution with n. = 20 will be the same as the standard error with n. = 50. II] . The sampling distribution of the mean will be approximately normal when or is large. I] . From the same population, the mean of the sampling distribution {pig} with n. = I" will be the same as the mean with n. =15. II] . The larger the sample size, the larger the difference between the mean of the sampling distribution and the population mean. I] . The sampling distribution is still assumed to be approximately normal if the underlying population is negatiyely skewed as long as the sample size is large. I] . The smaller the sample size, the larger the standard error. I] . The sampling distribution is always approximately normal even if the population is not normal. 1l.I"l."hich of the following statements about the sampling distribution of the mean {distribution of sample means} and the central limit theorem [BLT] are true? Select four [4} true statements from the list below: III . From the same population, the mean of the sampling distribution {#:E] with n = 4 will be equal to the mean with n. =12. III . The smaller the sample size, the smaller the standard error. D . The shape of the sampling distribution is closer to the population shape as the sample size increases. III . The sampling distribution is always approximately normal even if the population is not normal. or III . If pi = p. and 0's = T, then the distribution of sample means is normal. n. III . The smaller the sample size, the smaller the difference between the mean of the sampling distribution and the population mean. III . From the same population, the standard error of the sampling distribution with n = 41 will be smaller than the standard error with n = 1?. D t The sampling distribution of the mean will be approximately normal when sample size is large. III . If the population is non-normally distributed, then sample size does not matter for the central limit theorem to apply. III . The sampling distribution is still assumed to be approximately normal if the underlying population is non-normal as long as the sample size is large. III . If a population is perfectly normal, then for the distribution of sample means of any size, of, = pando' = or. In constructing a confidence interval for a population mean, which of the following are true? Select four [4} true statements from the list below: Note: A point: is deducted for each incorrect selection. D - If the point estimate and lower limit for a confidence interval are 142 and 134 respectively, then the upper limit must be 292. D - If a confidence interval does not contain the point estimate, then an error has been made in the calculation. D - Increasing the sample size will not change the width of the condence interval. D - A confidence interval that fails to capture the population mean will also fail to capture the sample mean. D - For a confidence level of 99%, the left-tail area an = 0.01. D - If a particular 34% confidence interval captures the population meanI then for the same sample data, the population mean will also be captured at the 35% confidence level. D - The width of the confidence interval depends on the size of the sample. D - If a confidence interval for the population mean is constructed from a sample of size n = 31], that interval must contain the population mean. D - Increasing the confidence level will not change the width of the condence interval. D - A 99% confidence interval must capture 99% of the sample values. D - A point estimate is a single population parameter that is used to estimate a sample statistic. D - For the same sample data, a 95% confidence interval will be narrower than a 99% confidence interval. In constructing a confidence interval for a population mean, which of the following are true'iI Select four [4} true statements from the list below: Note: A point: is deducted for each incorrect selection. I] - Increasing the sample size will reduce the width of the confidence interval. I] - Increasing the confidence level will not change the width of the confidence interval. I] - For the same sample data, a 95% confidence interval will be wider than a 99% confidence interval. I] - A condence interval that fails to capture the population mean will also fail to capture the sample mean. I] - If a confidence interval for the population mean is constructed from a sample of size n = 3i], that interval must contain the population mean. I] - If a confidence interval does not contain the point estimate, then an error has been made in the calculation. I] - For a confidence level of cuss, the left-tail area on 2 (ME. I] - If the point estimate and lower limit for a confidence interval are 1518 and 145.8 respectively, then the upper limit must be 159.8. I] - A 90% condence interval must capture gm; of the population values. I] - A point estimate is a single population parameter that is used to estimate a sample statistic. II] - If a particular 90% confidence interval captures the population mean, then for the same sample data, the population mean will also be captured at the 33% confidence level. II] - The width of the confidence interval depends on the size of the sample mean