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 29.8 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.) Sampling Scenario Z t could use either Z or t unclear (1) The sample has size 95, and it is from a non-normally distributed population with a known standard deviation of 3.2. (2) The sample has size 19, and it is from a population with a distribution about which we know very little.
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 29.8 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.)
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A t test will be used, when the population standard deviation is unknown and either the population distribution is normal or the sample size is large (> 30).
A z test will be used, when the population standard deviation is known and either the population distribution is normal or the sample size is large (> 30).
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