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8 for σ, 16 for the sample mean, and 15 for n.

Arrow down and enter 16.43 for μ 0 (null hypothesis). The sample data show there is sufficient evidence that Jeffrey's mean time to swim the 25-yard freestyle is less than 16.43 seconds. In other words, you do not think Jeffrey swims the 25-yard freestyle in 16.43 seconds but instead that he swims faster with the new goggles.Ĭonclusion: At the 5 percent significance level, we conclude that Jeffrey swims faster using the new goggles. Because the z-test is to the left of the critical z-value, we reject the null hypothesis. The critical z-value = –1.645 for this test has probability 0.05 to its left tail, according to the Normal Table (see Appendices). Make a decision: Since α > p-value, reject H 0.Īn alternative approach is to find the z-test corresponding to the sample mean x ¯ = 16. Because a 1.87 percent chance is small, the mean time of 16 seconds or less is unlikely to have happened randomly. Interpretation of the p-value: If H 0 is true, there is a 0.0187 probability (1.87 percent), that Jeffrey's mean time to swim the 25-yard freestyle is 16 seconds or less. The following examples illustrate a left-, right-, and two-tailed test. This makes the data analyst use judgment rather than mindlessly applying rules. Similarly, for a large p-value such as 0.4, as opposed to a p-value of 0.056 (alpha = 0.05 is less than either number), a data analyst should have more confidence that she made the correct decision in not rejecting the null hypothesis. Thinking about the meaning of the p-value: A data analyst should have more confidence that he made the correct decision to reject the null hypothesis with a smaller p-value (for example, 0.001 as opposed to 0.04) even if using the 0.05 level for alpha.H a never has a symbol that contains an equal sign.It is the key to conducting the appropriate test. The alternative hypothesis, H a H a, tells you if the test is left, right, or two-tailed.For this reason, we call the hypothesis test left, right, or two tailed. When you calculate the p-value and draw the picture, the p-value is the area in the left tail, the right tail, or split evenly between the two tails.