Homework 4, 1, 111: A Local Brewery Produces Three Premium L

Homework 4 1 111 A Local Brewery Produces Three Premium Lagers Nam

A local brewery produces three premium lagers named Half Pint, XXX, and Dark Night. Of its premium lagers, they bottle 40% Half Pint, 40% XXX, and 20% Dark Night lagers. In a marketing test of a sample of consumers, 36 preferred the Half Pint lager, 35 preferred the XXX lager, and 9 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, decide to retain or reject the null hypothesis that production of the premium lagers matches these consumer preferences using a 0.05 level of significance. State the value of the test statistic. (Round your answer to two decimal places.) = State the decision to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis. 2. A psychologist studying addiction tests whether cravings for cocaine and relapse are independent. The following table lists the observed frequencies in the small sample of people who use drugs. Obs. Freq. Relapse Yes No Cravings Yes No N = 58 (a) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.) = Decide whether to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis. (b) Compute effect size using Ï• and Cramer's V . Hint: Both should give the same estimate of effect size. (If necessary, round your intermediate steps to two or more decimal places. Round your answers to two decimal places.) Ï• = V = 3. A professor tests whether the loudness of noise during an exam (low, medium, and high) is independent of exam grades (pass, fail). The following table shows the observed frequencies for this test. Noise Level Low Medium High Exam Pass Fail N = 70 (a) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.) = Decide whether to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis. (b) Compute effect size using Cramer's V . (Round your answer to two decimal places.) V = 4. What is Cramer's V for each of the following values for the chi-square test for independence? (Round your answers to two decimal places.) (a) X2 = 7.49, n = 110, dfsmaller = 2 V = (b) X2 = 5.87, n = 80, dfsmaller = 1 V = (c) X2 = 12.61, n = 160, dfsmaller = 3 V = 5. Altamura, Dell'Osso, Vismara, and Mundo (2008) measured the relationship between gender and duration of untreated illness among a sample of those suffering from major depressive disorder. The following table lists the observed frequencies from this study. Duration of Untreated Illness ≤ 12 Months > 12 Months Gender Men Women N = 113 Compute a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.) = Decide whether to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis. 6. Which nonparametric tests can be computed using a normal approximation formula to compute the test statistic? (Select all that apply.) sign test Wilcoxon signed-ranks T test Kruskal-Wallis H test Mann-Whitney U test Friedman test 7. A community psychologist selects a sample of 16 local police officers to test whether their physical endurance is better than the median score of 72. She measures their physical endurance on a 100-point physical endurance rating scale. Performance Scores Based on the data given above, compute the one-sample sign test at a 0.05 level of significance. x = State whether to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis. 8. Practitioners measured spiritual well-being (SWB) in a sample of 16 adults who were alcoholic before and following treatment for alcoholism. Change in SWB Following Treatment +9 +11 -8 -3 -5 +7 +20 +14 -6 +12 +15 +13 -1 -4 -2 +10 Use the normal approximation for the Wilcoxon signed-ranks T test to analyze the data above. (Round your answer to two decimal places.) z = State whether to retain or reject the null hypothesis. (Assume alpha equal to 0.05.) Retain the null hypothesis. Reject the null hypothesis. 9. A professor has a teaching assistant record the amount of time (in minutes) that a sample of 16 students engaged in an active discussion. The assistant observed 8 students in a class who used a slide show presentation and 8 students in a class who did not use a slide show presentation. With Microsoft PowerPoint Without Microsoft PowerPoint Use the normal approximation for the Mann-Whitney U test to analyze the data above. (Round your answer to two decimal places.) z = State whether to retain or reject the null hypothesis. (Assume alpha equal to 0.05.) Retain the null hypothesis. Reject the null hypothesis. 10. A statistics instructor measured student attitudes toward a statistics course prior to lectures, at the midterm, and after the final exam. Attitudes were measured on a 16-point scale, with higher scores indicating more positive attitudes toward the statistics course. Student Prior to Lectures At the Midterm After the Final A B C D E Based on the results shown in the table, test whether or not attitudes differed using the Friedman test at a 0.05 level of significance. (Round your answer to two decimal places.) = State whether to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis. 11. An instructor tests whether class attendance (low, average, high) and grade point average (low, average, high) are independent. State the degrees of freedom for the test. df =

Homework 4 1 111 A Local Brewery Produces Three Premium Lagers Nam

A local brewery produces three premium lagers named Half Pint, XXX, and Dark Night. Of its premium lagers, they bottle 40% Half Pint, 40% XXX, and 20% Dark Night lagers. In a marketing test of a sample of consumers, 36 preferred the Half Pint lager, 35 preferred the XXX lager, and 9 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, decide to retain or reject the null hypothesis that production of the premium lagers matches these consumer preferences using a 0.05 level of significance. State the value of the test statistic. (Round your answer to two decimal places.) = State the decision to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis.

Paper For Above instruction

The objective of this analysis was to evaluate whether the production proportions of three premium lagers—Half Pint, XXX, and Dark Night—align with consumer preferences. The given production distribution indicates 40% for Half Pint, 40% for XXX, and 20% for Dark Night. In the sample, 36 consumers preferred Half Pint, 35 preferred XXX, and 9 preferred Dark Night. The null hypothesis (H₀) assumes that the observed consumer preferences match these production proportions, and the alternative hypothesis (H₁) suggests discrepancies exist. The test employed is the chi-square goodness-of-fit, which compares observed frequencies to expected frequencies based on the assumed proportions.

Calculating expected frequencies for each lager involves multiplying the total sample size by the proportions: total sample = 36 + 35 + 9 = 80 consumers. Expected frequencies are therefore:

  • Half Pint: 80 * 0.40 = 32
  • XXX: 80 * 0.40 = 32
  • Dark Night: 80 * 0.20 = 16

Next, the chi-square test statistic is calculated using the formula: χ² = Σ[(O - E)² / E], where O represents observed frequencies, and E represents expected frequencies. Applying this formula yields:

χ² = (36 - 32)² / 32 + (35 - 32)² / 32 + (9 - 16)² / 16

= (4)² / 32 + (3)² / 32 + (-7)² / 16

= 16 / 32 + 9 / 32 + 49 / 16

= 0.5 + 0.28125 + 3.0625

= 3.84375

The calculated chi-square statistic is approximately 3.84 (rounded to two decimal places). The degrees of freedom for this test are calculated as the number of categories minus 1, thus df = 3 - 1 = 2. The critical value of χ² at α=0.05 with 2 degrees of freedom is approximately 5.99.

Since the computed χ² (3.84) is less than the critical value (5.99), we fail to reject the null hypothesis. This indicates there is not enough evidence to conclude a significant difference between consumer preferences and the production proportions of the lagers.

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