Suppose that we want to estimate the mean reading speed of second graders. The r

Question

Suppose that we want to estimate the mean reading speed of second graders. The random sample of students reading speeds we choose has a mean of 31.5 words per minute and a standard deviation of 2.7 words per minute. 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.)

Explanation / Answer

when population standard deviation is known , we use z-test .

if population standard deviation is not known , but sample size is greater than 30 , we can use both t-test . and z-test

if sample-size is less than 30 , we have to use t-test only

1) population standard deviation is known - z-test

2) population standard deviation is known , n > 30 , z-test

3)population standard deviation is not known , but n >30 , hence z or t-test

4) n < 30 , population standard deviation is not known , and not normal , so unclear

5) population standard deviation is unknown , n < 30 - t-test

1)

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