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 499 and a standard deviation of 74. 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.) The sample has size 19, and it is from a normally distributed population with unknown standard deviation The sample has size 13, and it is from a population with a distribution about which we know very little The sample has size 95, and it is from a non-normally distributed population with a known standard deviation of 77. The sample has size 15, and it is from a normally distributed population with a known standard deviation of 77. The sample has size 110, and it is from a non-normally distributed population.

Explanation / Answer

1.) We will use t-test because n < 30 and standard deviation is unknown.

2.) It is unclear because in this situation we can not use either of the tests. Sample size has to be large enough if we want to use either of the tests for a non-normally distributed population.

3.) We can use Z-test because we have large enough sample size,i.e. 95, and we also know the population standard deviation.

4.) We will use Z-test because we know the population standard deviation.

5.) We can use t-test because sample size it large enough to use it even for a non-normally distributed population.

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