Nielsen reported that young men in the United States watch 56.2 minutes of prime time TV daily. A researcher believes that young men in Germany spend more time watching prime TV. A sample of German young men will be selected by the researcher, and the time they spend watching TV in one day will be recorded. The sample results will be used to test the following null and alternative hypotheses. Ho: μ ≤ 56.2 Ha: μ > 56.2 a). What is the Type 1 error in this situation? What are the consequences of making this error? b). What is the Type 2 error in this situation? What are the consequences of making this error?
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Step 1
A Type 1 error occurs when the null hypothesis is true, but is rejected. In this situation, a Type 1 error would occur if the researcher concludes that German young men watch more than 56.2 minutes of prime time TV daily, when in reality, they do not. The Show more…
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Nielsen reported that young men in the United States watch 56.2 minutes of prime-time TV daily (The Wall Street Journal Europe, November 18,2003 ). A researcher believes that young men in Germany spend more time watching prime-time TV. A sample of German young men will be selected by the researcher and the time they spend watching TV in one day will be recorded. The sample results will be used to test the following null and alternative hypotheses. \[ \begin{array}{l} H_{0}: \mu \leq 56.2 \\ H_{\mathrm{a}}: \mu>56.2 \end{array} \] a. What is the Type I error in this situation? What are the consequences of making this error? b. What is the Type II error in this situation? What are the consequences of making this error?
Nielsen reported that young men in the United States watch 56.2 minutes of prime-time TV daily (The Wall Street Journal Europe, November $18,2003$ ). A researcher believes that young men in Germany spend more time watching prime-time TV. A sample of German young men will be selected by the researcher and time they spend watching TV in one day will be recorded. The sample results will be used to test the following null and alternative hypotheses. $$\begin{aligned} H_{0} : \mu & \leq 56.2 \\ H_{\mathrm{a}} : \mu &>56.2 \end{aligned}$$ a. Whatis the Type Iemorinthissituation? What are the consequencesofmakingthiserror? b. Whatis the Type Ilerrorinthis situation? Whataretheconsequencesof makingthis error?
A recent article in Healthy Life magazine claimed that the mean amount of leisure time per week for European men is 48.2 hours. The distribution of leisure time amounts is reported to be approximately Normal. You believe the figure of 48.2 is too large and decide to conduct your own test. In a random sample of 25 European men, you find that the mean is 44.6 hours of leisure per week and that the standard deviation of the sample is 6.9 hours. (a) State the null hypothesis and the alternative hypothesis for your test. (b) Conduct the test and determine the p-value. At 0.01 significance level, can you conclude that the information in the article is untrue? (c) How would your answer to part (b) be affected if the distribution of leisure time amounts was uniform?
Sheryl E.
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