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

Question

Suppose that we want to estimate the mean score on a nationwide examination in anthropology, and for this purpose we choose a rand scores. The sample we choose has a mean of 510 and a standard deviation of 71. For each of the following sampling scenarios, determine which te is appropriate to use when making inference statements about the population mean. om sample (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 Z or unclear (1) The sample has size 20, and it is from a normally distributed population with unknown standard deviation. (2) The sample has size 85, and it is from a non- normally distributed population (3) The sample has size 13, and it is from a population with a distribution about which we knowO very little. (4) The sample has size 14, and it is from a normally distributed population with a known standard deviation of 75 (5) The sample has size 80, and it is from a non- normally distributed population with a known standard deviation of 75 Worked Example

Explanation / Answer

1) as sample size is less than 30 and std deviation is unknown ----- t distribution

2)as sample size is higher than 30 --------- could use either Z or t

3) as population distribution is unknown and sample size is less than 30 ------ unclear

4)here as std deviation is known and distribution is normal ---------Z distribution

5)here as sample size is higher with known population std deviaiton--------Z distribution

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