Chapter Nine Show All Work Problem 1A Skeptical Paranormal R

Chapter Nineshow All Workproblem 1a Skeptical Paranormal Researcher C

Chapter Nineshow All Workproblem 1a Skeptical Paranormal Researcher C

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. 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. Problem 3) A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis? 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? Problem 5) What is the difference between an Type I and a Type II error? Provide an example of both. 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 “The 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 “made them very sad” to 10 indicating that it “made them very happy.” Steve computes the total scores from each student and created a variable called “hapsad.” 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? 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 349 of your textbook, under Hypothesis Tests with the t Distribution to conduct SPSS or Excel analysis). Problem 2) Billie wishes to test the hypothesis that overweight individuals tend to eat faster than normal-weight individuals. 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 record the amount of time it takes them to eat the Big Mac special. Data are recorded for 10 overweight and 10 normal weight Big Mackers: 1.0, 585.0, 1.0, 540.0, 1.0, 660.0, 1.0, 571.0, 1.0, 584.0, 1.0, 653.0, 1.0, 574.0, 1.0, 569.0, 1.0, 619.0, 1.0, 535.0, 2.0, 697.0, 2.0, 782.0, 2.0, 587.0, 2.0, 675.0, 2.0, 635.0, 2.0, 672.0, 2.0, 606.0, 2.0, 789.0, 2.0, 806.0. a) Compute an independent-samples t-test on these data. Report the t-value and the p-values. Were the results significant? b) What is the difference between the mean of the two groups? What is the difference in the standard deviation? c) What is the null and alternative hypothesis? Do the data results lead you to reject or fail to reject the null hypothesis? d) What do the results tell you? Problem 3) Lilly collects data on a sample of 40 high school students to evaluate whether the proportion of female high school students who take advanced math courses varies depending upon whether they have been raised primarily by their father or by both their mother and their father. Two variables are found: math (0 = no advanced math, 1 = some advanced math) and Parent (1= primarily father, 2 = father and mother). a) Conduct a crosstabs analysis to examine whether the proportion of female high school students who take advanced math differs for different parent variables. b) What percent of female students took advanced math? c) What percent of female students did not take advanced math when raised by just their father? d) What are the Chi-square results? Are the results significant? What do they mean? e) What are your null and alternative hypotheses? Did the results lead you to reject or fail to reject the null and why? Problem 4) This problem will introduce the technique called Analysis of Variance. Use the following data to conduct a One-Way ANOVA: Scores grouped into three different groups. The scores are dependent variables with the group (independent variable). a) What is the F-score; are the results significant, and at what level (P-value)? b) If significant, conduct the post hoc test (Tukey) and explain between which groups the significance occurred. c) What do the results from the test mean?

Paper For Above instruction

The set of problems presented spans various fundamental statistical tests used in research, emphasizing the importance of formulating hypotheses, conducting appropriate tests, and interpreting the results in context. These methods include hypothesis testing for proportions, t-tests for means, chi-square tests for categorical variables, and analysis of variance (ANOVA). These techniques form the backbone of empirical research, allowing researchers to infer whether observed differences or relationships are statistically significant or attributable to random variation.

Null and Alternative Hypotheses in Hypothesis Testing

Hypothesis formulation is the first step in any statistical inference. For example, in Problem 1, the paranormal researcher hypothesizes that the proportion of Americans who have seen a UFO is less than 1 in 1000. The null hypothesis (H₀) typically posits no effect or status quo, while the alternative hypothesis (H₁ or Ha) presents the effect or claim to be tested. Here, H₀ would state that the proportion is equal to or greater than 1/1000, expressed as p ≥ 0.001, while H₁ would state that the proportion is less than 1/1000, or p

Conducting and Interpreting T-Tests

The detailed procedures for calculating t-tests involve computing the test statistic based on sample means, standard deviations, and sample sizes. For the one-sample t-test in Problem 1, the researcher compares the sample mean to a known population mean, using the formula for the t-statistic. The significance of the test depends on the p-value, which is derived from the t-distribution. A p-value less than the significance level (commonly 0.05) indicates rejection of the null hypothesis. In Problem 1a, the calculation suggests whether the observed sample mean significantly differs from the population mean of 6.

In Problem 2, the independent-samples t-test compares the means of two independent groups (overweight and normal weight Big Mackers). The calculation considers differences in means, pooled standard deviations, and sample sizes. The significance determines if the observed difference in eating times is statistically meaningful, supporting or refuting the hypothesis that overweight individuals eat faster.

Chi-Square Tests for Categorical Data

The chi-square test evaluates whether there is a significant association between categorical variables. In Problem 3, the chi-square test for independence examines whether the proportion of females taking advanced math varies with parental influence. The observed frequencies are compared to expected frequencies under the null hypothesis that the variables are independent. A significant chi-square statistic indicates a relationship, while a non-significant result suggests no association.

Moreover, calculating percentages helps interpret proportions, for instance, the percentage of students taking math or not. The chi-square results, including expected counts and chi-square values, inform whether the observed data significantly deviate from the expectation under the null hypothesis, leading to conclusions about the relationship.

Analysis of Variance (ANOVA)

The One-Way ANOVA extends t-test capabilities to compare three or more group means simultaneously. In Problem 4, the scores are divided into three groups. The ANOVA tests whether at least one group mean differs significantly from the others by analyzing variances within and between groups. The F-statistic indicates the relative magnitude of between-group variance to within-group variance; a higher F suggests greater differences.

If the ANOVA result is significant (p

Errors in Hypothesis Testing

Understanding potential errors in hypothesis testing is critical for correct interpretation. A Type I error occurs when the null hypothesis is incorrectly rejected (false positive), implying there is an effect when there isn't. For example, concluding that UFO sightings are less than 1 in 1000 when they are not. Conversely, a Type II error involves failing to reject a false null hypothesis (false negative), such as not detecting a true decrease in average television watching time.

Proper study design and significance level choices aim to minimize these errors, but balancing the risks of false positives and negatives remains a fundamental concern in statistical inference.

Conclusion

These statistical methods—hypothesis testing, chi-square analysis, and ANOVA—are vital tools for analyzing data across diverse research disciplines. Each technique provides a way to infer if observed patterns are statistically significant, supporting or challenging hypotheses. Correct application and interpretation of these tests enable researchers to draw valid conclusions, advancing knowledge and informing decision-making. Whether assessing proportions, comparing means, or exploring associations among categorical variables, these procedures form the foundation of empirical evidence in scientific inquiry.

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