A researcher tests whether listening to music while taking a test has any effect. The population mean of people taking an exam while not listening to music is 50, with a standard deviation of 12. The researcher tests a sample of 57 people who listen to music while taking a test and they produce a mean of 54.36. Using a two-tailed test with a p-value of .05 the critical value is -1.96 and 1.96. Make a decision about your hypothesis? Using a one-tailed test with a p-value of .05. the critical value is -1.65 and 1.65. Make a decision about your hypothesis?
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Given: Population mean (μ) = 50 Population standard deviation (σ) = 12 Sample mean (X̄) = 54.36 Sample size (N) = 57 Calculate the z-score: \[ z = \frac{X̄ - μ}{\frac{σ}{\sqrt{N}}} \] \[ z = \frac{54.36 - 50}{\frac{12}{\sqrt{57}}} \] \[ z = \frac{4.36}{1.587} Show more…
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Listening to music while taking a test may be relaxing or distracting. We test 49 participants while listening to music and they produce a M = 54.36. The mean of the population taking this test without music is μ = 50 (σ = 12). a. Does listening to music while taking the test lead to a significant difference in scores? Conduct a full hypothesis test using the .05 level of significance. b. Compute the effect size with Cohen's d c. What is the probability that we made a type I error? What would be the error in terms of independent and dependent variables? d. Is there a risk of a Type II error? e. Summarize your findings in APA format
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A researcher is testing the hypothesis that the proportion of people in a certain sub-population who have a particular characteristic differs from the proportion in the general population, known to be .30. In a random sample of 100 people from the sub-population, the sample proportion was .25. The researcher performed a two-tailed hypothesis test at the .05 significance level. Which of the following is the critical region for the test? Z < -1.96, Z > 1.96 Z < -1.64, Z > 1.64 Z < -1, Z > 1 Z < -.05, Z > .05 Can not tell based on the information given
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