SmalleyTylerStatsHomeworkWeek5

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California Baptist University *

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114

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Statistics

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Jan 9, 2024

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STA 144 Week 5 Homework Work on the following problem set from chapters 9-10 Chapter 9 1. Why is significance an important construct in the study and use of inferential statistics? a. Significance is how accurate the testing results were based on the test itself and not other factors outside of your control. 2. What is statistical significance? a. The degree of risk one is willing to take that they will reject a null hypothesis if it turns out to be true. 3. What does the (idea of the) critical value represent? a. The basis for whether or not to accept the null hypothesis 4. Given the following information, would your decision be to reject or fail to reject the null hypothesis? Setting the level of significance at .05 for decision making, provide an explanation for your conclusion. a. The null hypothesis that there is no relationship between the type of music a person listens to and his propensity for crime (p < .05) a. This would show that the null hypothesis is true and the study found that there is in fact no correlation between a type of music someone listens to and their propensity for crime. b. The null hypothesis that there is no relationship between the amount of coffee consumption and GPA (p = .62) a. This test would show that the null hypothesis should be rejected as there is at least some level of relationship between coffee and GPA c. The research hypothesis that a negative relationship exists between the number of hours worked and level of job satisfaction (p = .51) a. This study would also reject the null hypothesis and perhaps show better correlating numbers using a positive relationship with number of hours worked and job satisfaction

6. Why is it “harder” to find a significant outcome (all other things being equal) when the research hypothesis is being tested at the .01 rather than the .05 level of significance? This is because .01 is a much stricter number with less room for error where as .05 may give some more room to breathe when trying to stay within those ranges. 7. Why should we think in terms of “failing to reject” the null, rather than just accepting it? Because there is also the chance to test and retest to attempt to try other ways of rejecting. Failing to reject shows that there is still a possibility of fixing your test where as accepting it is saying you basically give up and will not do further testing. 8 . What does chance have to do with testing the research hypothesis for significance ? Chance is factors that may cause a difference between groups that cannot be explained by the testing procedure or systematic influences. Understanding the possibility of chance affecting your study is important so that certain outcomes are neither rejected or accepted immediately as chance may have interfered with the results. Chapter 10 1. When is it appropriate to use the one-sample Z-test? a. When you are simply testing the differences between a sample and a population as well as a test involving one group only. 2. What’s with the z in Z-test? What similarity does it have to a simple z or standard score? a. The Z test is a test to determine whether population means are different when the variances are known as well as the sample size being larger. This hypothesis test includes the z score as the number that represents the results from the z test. 3. For the following situations, write out in words a research hypothesis: a. Bob wants to know whether the weight loss for his group on the chocolate-only diet is representative of weight loss in a large population of middle-aged men. a. Null Hypothesis – Chocolate only diet will have no effect on weight loss for middle aged men. b. Hypothesis – Several sample sizes of 100 middle aged men will be tested on a chocolate only diet to determine the effect it has on weight loss.

b. The health department is charged with finding out whether the rate of flu per thousand citizens during this past flu season is comparable to the average rate during the past 50 seasons. a. Null Hypothesis – There is no correlation between this year’s flu season and the last 50 years. b. Hypothesis – A set of sampled tests among the public will survey the participants on whether or not they have had the flu during the most recent flu season and this will determine the rate at which it relates to the previous 50 years of flue seasons. c. Blair is almost sure that his monthly costs for the past year are not representative of his average monthly costs over the past 20 years. a. Null Hypothesis – The current monthly costs are the same as they have always been for Blair b. Hypothesis – We will look at the sample sizing of each year for Blair and determine the mean of his monthly costs and compare it to the current costs to figure out the differences there may be between them.

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SmalleyTylerStatsHomeworkWeek5

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