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# day19 - Hypothesis Tests for Known One-Tailed Tests Lower...

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Hypothesis Tests for μ - Known σ One-Tailed Tests Lower Tail Test H 0 : μ μ 0 H a : μ < μ 0 Upper Tail Test H 0 : μ μ 0 H a : μ > μ 0 Example : Individuals filing federal income tax returns prior to March 31 re- ceived an average refund of \$1056. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (April 10 to April 15). A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. We want to test this claim. For a sample of 400 individuals who filed a tax return between April 10 and April 15, the sample mean refund was \$910. Based on prior experience a population standard deviation of σ = \$1600 may be assumed. 1. Specify the null and alternative hypotheses. Ex : 1

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2. Specify the probability of making a Type I error. This number is de- noted by α and is called the level of significance. Ex : 3. Compute the test statistic. The test statistic is a measure of how far the sample mean ¯ x is from the hypothesized value μ 0 . We use the sampling distribution of ¯ x to obtain the test statistic.
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