DB Week #5

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Apr 3, 2024

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DB Week #5 In the report being prepared for an editorial in the San Francisco Chronicle, the random sample showed 210 out of 300 random households’ own pets. On the surface, these numbers could be divided to show that .7 or 70% of the U.S. population are pet owners, but we can use the .05 level of significance to more accurately represent the data. “The most common level, used to mean something is good enough to be believed, is .95. This means that the finding has a 95% chance of being true” (Creative Research Systems, 2016, para. 5). The .05 significance level. The problem provided is a binomial distribution according to our textbook. “The binomial conditions are met: (a) there are only two possible outcomes (a particular call is either dropped or not dropped), (b) there are a fixed number of trials (6), (c) there is a constant probability of success (.05), and (d) the trials are independent” (Lind et al., 2019, p.168). Under binomial conditions the p ± z√ (p (1 – p)/n) formula can be applied. Then we can plug the data from the problem into the formula and solve: .70 ± 1.96√ (.70 (1 – .70)/300) .70 ± 1.96√ (.0007) .70 ± .052 The confidence intervals of this data set are 75.2% and 64.8%. The study by the American Pet Food Dealers Association stated that “63% of U.S. households own pets,” which does not fall within the confidence intervals that were determined. Therefore, the statement is rejected. Based on the people around me and the majority of them being pet owners, I think that they accurately represent the consumer base for the U.S. pet food industry.

While confidence intervals are used in everyday life especially for professionals for things such as test results from a doctor visit or political polls, we also rely on the word of God to give us confidence. Philippians 1:6 states, “Being confident of this very thing, that he which hath begun a good work in you will perform it until the day of Jesus Christ” (King James Version). Since individuals cannot reasonably rely on statistical data for every decision in everyday life, confidence in God and having faith in Him should be our guide. Through prayer and devotion to the word of Christ, we can eliminate the doubts and fears in our lives. Isaiah 41:10 “Fear not, for I am with you; be not dismayed, for I am your God…” (English Standard Version). References Creative Research Systems. (2016). Significance in statistics and surveys. Creative Research Systems. https://www.surveysystem.com/signif.htm#:~:text=To%20find%20the%20 significance%20level,01%3D . Lind, D., Marchal, W., & Wathen, S. (2019). Basic statistics for business & economics. McGraw-Hill Education.

Matthew, I found your statistical example of lying and your application to scripture very informative. I wanted to share an interesting article by Stetzer that demonstrates how statistics can benefit Christian ministry. According to Stetzer (2016), three uses of stats in ministry are:  helping to define reality.  helping to teach others.  helping leaders make strategical decisions. When used to define reality, statistics can provide a starting point for Christian leaders when fellowshipping to others through offering information about people's thoughts and behaviors (Stetzer, 2016). Statistics also help to teach people. For example, a study on how different churches react to different situations can benefit church leaders (Stetzer, 2016). Finally, using statistics in ministry can help leaders make strategical decisions, such as helping Christians use God's gifts (Stetzer, 2016). This is a brief summary of the particularly beneficial use of statistics as Christians that bring glory to God. "Do your best to present yourself to God as one approved, a worker who has no need to be ashamed, rightly handling the word of truth" (2 Timothy 2:15, ESV). References Stetzer, E. (2016, July 27). Why you should use stats in ministry. Christianity Today. https://www.christianitytoday.com/edstetzer/2016/july/how-to-use-stats.html

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Natasha, Great display of the formulas you used to calculate the results. Our textbook defines confidence intervals as “a range of values constructed from sample data so that the population parameter is likely to occur within that range at a specified probability” (Lind et al., 2019, p. 244). Chief Marketing Scientist, Bruce Duncan, explains the importance of confidence intervals in his article. When reporting data without confidence intervals, confidence risk increases, and there can be an overrepresentation of results (Duncan, 2015). Confidence intervals limit the uncertainty of a data set and are important for accurate market research reports (Duncan, 2015). “Good research provides information and understanding which allows us to more effectively value our alternatives and make better decisions” (Duncan, 2015, para. 1). References Duncan, B. (2015, November 12). Importance of confidence intervals. Insights Association. https://www.insightsassociation.org/article/importance-confidence-intervals Lind, D., Marchal, W., & Wathen, S. (2019). Basic statistics for business & economics. McGraw-Hill Education.

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