Suppose that we want to estimate the mean score on a nationwide examination in b

Question

Suppose that we want to estimate the mean score on a nationwide examination in biology, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of 519 and a standard deviation of 78. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean. (In the table, Z refers to a variable having a standard normal distribution, and t refers to a variable having a t distribution.) could use Sampling Scenario t either either Z ort unclear (1) The sample has size 100, and it is from a non-normally distributed population. (2) The sample has size 15, and it is from a normally distributed population with unknown standard deviation. (3) The sample has size 90, and it is from a non-normally distributed population with a known standard deviation of 76 (4) The sample has size 14, and it is from a normally distributed population with a known standard deviation of 76. (5) The sample has size 12, and it is from a population with a distribution about which we know very little Clear Undo Help

Explanation / Answer

From the given data we have

t - value for 95% CI = 2.31

Lower limit = -0.19 - 2.31*1.7831/sqrt(9) = -1.563

upper limit = -0.19 + 2.31*1.7831/sqrt(9) = 1.183

Mean -0.19 std. dev. 1.783094

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