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

Question

Suppose that we want to estimate the mean score on a nationwide examination in psychology, and for this purpose we choose a scores. The sample we choose has a mean of 489 and a standard deviation of 78. For each of the following sampling scenarios, determine which is appropri ate to use when making inference statements about the population mean. test statistic (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 Z t either Z or unclear (1) The sample has size 105, and it is from a non- normally distributed population with a known standard deviation of 78 (2) The sample has size 18, and it is from a population with a distribution about which we knowEE very little (3) The sample has size 11, and it is from a normally distributed population with a known standard deviation of 78. (4) The sample has size 80, and it is from a non- normally distributed population. (5) The sample has size 16, and it is from a normally distributed population with unknown standard deviation. Submit Ass Worked Example

Explanation / Answer

1)hre as sample size is large and std deviation is know ; -------Z distribution

2) as sample size is lowr than 30 and population distribution not known ------ unclear

3)for known std deviaiton and population distirbution is normal -------Z distribution

4) as normal distribution and sample size is large ----could use either Z or t

5)as sample size is small and std deviation is unknown ----- t distribution

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