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Data File 5: Statistical Hypothesis Testing: A Comprehensive Analysis of Proportions, Means, and Errors

Covers statistical hypothesis testing.

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    Data File 5 : Statistical Hypothesis Testing: A Comprehensive Analysis of Proportions, Means, and Errors Data File 5 Chapter Nine Show all work Problem 1) A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand. State the null hypothesis and the alternative hypothesis for a test of significance. Here we want to test whether the statement made by the paranormal researcher is true or not thus the null and alternative hypothesis are, 𝐻 0 : 𝑝 β‰₯ 1 1000 π‘Žπ‘›π‘‘ 𝐻 π‘Ž : 𝑝 < 1 1000 Problem 2) At one school, the average amount of time that tenth - graders spend watching television each week is 18.4 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased. Formulate the null and alternative hypotheses for the study described. Here the null and alternative hypotheses for the study are, 𝐻 0 : ΞΌ β‰₯ 18 . 4 π‘Žπ‘›π‘‘ 𝐻 π‘Ž : ΞΌ < 18 . 4 Problem 3) A two - tailed test is conducted at the 5% significance level. What is the P - value required to reject the null hypothesis? We reject the null hypothesis if the p - value is smaller than the significance level thus here we would reject the null hypothesis if p - value is smaller than 5% or 0.05. Problem 4) A two - tailed test is conducted at the 5% significance level. What is the right tail percentile required to reject the null hypothesis?

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    As the test is two tailed so we would reject the null hypothesis if the right tail percentile is smaller than 5%/2 = 2.5% or 0.025. Problem 5) What is the difference between an Type I and a Type II error? Provide an example of both. A Type I error is rejecting the null hypothesis which is actually true and a Type II error is accepting a null hypothesis which is actually false. Suppose we want to test whether a new medication is better than old medication or not. If we reject the null hypothesis and decide the new medication is better when actually the old medication is better (or has no difference) we will make a Type I error. And if we fail to reject the null hypothesis and decide the old medication is better or indifference where actually the new medication is better we would make a Type II error. Chapter 10 Show all work Problem 1) Steven collected data from 20 college students on their emotional responses to classical music. Students listened to two 30 - second segments from β€œThe Collection from the Best of Classical Music.” After listening to a segment, the students rated it on a scale from 1 to 10, with 1 indicating that it β€œmade them very sad” to 10 indicating that it β€œmade them very happy.” Steve computes the total scores from each student and created a variable called β€œhapsad.” Steve then conducts a one - sample t - test on the data, knowing that there is an established mean for the publication of others that have taken this test of 6. The following is the scores: 5.0 5.0 10.0 3.0 13.0 13.0 7.0 5.0 5.0 15.0 14.0 18.0 8.0 12.0 10.0 7.0 3.0 15.0 4.0 3.0 a) Conduct a one - sample t - test. What is the t - test score? What is the mean? Was the test significant? If it was significant at what P - value level was it significant?

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    The obtained SPSS output is given below, One - Sample Statistics N Mean Std. Deviation Std. Error Mean hapsad 20 8.7500 4.73370 1.05849 One - Sample Test Test Value = 6 t df Sig. (2 - tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper hapsad 2.598 19 .018 2.75000 .5346 4.9654 From the above output we can see that t - test score is 2.598 and the mean is 8.75. The output suggests that the test is significant at any significance level more than 0.018 because the p - value is 0.018. b) What is your null and alternative hypothesis? Given the results did you reject or fail to reject the null and why? ( Use instructions on page 437 of your textbook, under Hypothesis Tests with the t Distribution to conduct SPSS or Excel analysis). Here the claimed mean was 6 hence the null and alternative hypotheses are, 𝐻 0 : ΞΌ = 6 π‘Žπ‘›π‘‘ 𝐻 π‘Ž : ΞΌ β‰  6 As the test was significant so the null hypothesis was rejected. Problem 2 ) Billie wishes to test the hypothesis that overweight individuals tend to eat faster than normal - weight individuals. To test this hypothesis, she has two assistants sit in a McDonald’s restaurant and identify individuals who order the Big Mac special for lunch. The Big Mackers as they become known are then classified by the assistants as overweight, normal weight, or neither overweight nor normal weight. The assistants identify 10 overweight and 10 normal weight Big Mackers. The assistants record the amount of time it takes them to eight the Big Mac special. 1.0 585.0 1.0 540.0 1.0 660.0 1.0 571.0 1.0 584.0

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