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Factors that might influence statistical power include: choosing a significance level. Significance levels such as: 05 and .01 are commonly used among researchers. According to Cozby (2009), “The significance level chosen by the researcher usually is dependent on the consequence of making a Type I error versus a Type II error” (pg. 259). Random errors usually carry a lower significance level than those previously mentioned, however “a meaningful result is more likely to be overlooked when the significance level is very low” (Cozby, 2009, pg. 260). Aside from choosing a significance level, a Type II error could be due to a small sample size or a small effect size. If the sample size is too small there is a possibility that no relationship may be determined and if there is a relationship, it may be easily overlooked. The problem with a small effect size is that according to Cozby (2009), “Very small effect sizes are difficult to detect without a large sample size” (pg. 260). Therefore, researchers should make sure that the significance level, effect size, and sample size reflect an appropriate size in order to receive accurate results thus eliminating the possibility of Type I and/or Type II errors occurring.

Cozby, P.C. (2009).

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...Type I error (or, error of the first kind) and Type II error (or, error of the second kind) are precise technical terms used in statistics to describe particular flaws in a testing process, where a truenull hypothesis was incorrectly rejected (Type I error) or where one fails to reject a false null hypothesis (Type II error). The terms are also used in a more general way by social scientists and others to refer to flaws in reasoning. This article is specifically devoted to the statistical meanings of those terms and the technical issues of the statistical errors that those terms describe. Statistical test theory In statistical test theory the notion of statistical error is an integral part of hypothesis testing. The test requires an unambiguous statement of a null hypothesis, which usually corresponds to a default "state of nature", for example "this person is healthy", "this accused is not guilty" or "this product is not broken". An alternative hypothesis is the negation of null hypothesis, for example, "this person is not healthy", "this accused is guilty" or "this product is broken". The result of the test may be negative, relative to null hypothesis (not healthy, guilty, broken) or positive (healthy, not guilty, not broken). If the result of the test corresponds with reality, then a correct decision has been made. However, if the result of the test does not correspond with reality, then an error has occurred. Due to the statistical nature of a test, the result is never...

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...Which statement is NOT true concerning the t distribution? Select one: a. Compared to the normal distribution, the t distribution has more area in the tails and less in the center. b. As the number of degrees of freedom increases, the t distribution approaches the normal distribution. Incorrect c. The t distributions are skewed to the left. d. The population variance is unknown and is estimated by the sample variance s2. e. As the sample size increases beyond 120, the t and Z distributions are indistinguishable. Feedback The correct answer is: The t distributions are skewed to the left. Question 2 Incorrect Mark 0 out of 1 Not flaggedFlag question Question text Which of the following involves a test of two-independent samples? Select one: a. Test of differences in the percent of men and women who are or are not members of Greek organizations on campus b. Test of the average incomes of magazine subscribers of Southern Living verses Better Homes and Gardens c. Test of whether the mean salary of professors at Metro University is higher than the national average for university professors Incorrect d. Test of whether a change occurred in the likelihood of heart disease among people who switched to a diet high in fish e. Test of differences in ad recall among three experimental groups (each of which saw a different advertisement) and a control group Feedback The correct answer is: Test of the average incomes of magazine subscribers of Southern Living verses Better...

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...what is the probability of a type one error? z=(225-180)/20=2.25; the corresponding tail area is .0122, which is the probability of a type I error. If the cholesterol level of healthy men is normally distributed with a mean of 180 and a standard deviation of 20, at what level (in excess of 180) should men be diagnosed as not healthy if you want the probability of a type one error to be 2%? 2% in the tail corresponds to a z-score of 2.05; 2.05 × 20 = 41; 180 + 41 = 221. Type II error A type II error occurs when one rejects the alternative hypothesis (fails to reject the null hypothesis) when the alternative hypothesis is true. The probability of a type II error is denoted by *beta*. One cannot evaluate the probability of a type II error when the alternative hypothesis is of the form µ > 180, but often the alternative hypothesis is a competing hypothesis of the form: the mean of the alternative population is 300 with a standard deviation of 30, in which case one can calculate the probability of a type II error. Examples: If men predisposed to heart disease have a mean cholesterol level of 300 with a standard deviation of 30, but only men with a cholesterol level over 225 are diagnosed as predisposed to heart disease, what is the probability of a type II error (the null hypothesis is that a person is not predisposed to heart disease). z=(225-300)/30=-2.5 which corresponds to a tail area of .0062, which is the probability of a type II error...

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...Individual Assignment: Understanding Business Research Terms and Concepts: Part 3 Instructions Please highlight (like I just did) the correct answer and upload the entire document to the Assignments link by the due date in the syllabus. This is the only version of the assignment that will be graded. Do not use the matching shown on the Materials tab page for Week 5! 1 Which of the following shapes best represents a normal distribution as it is depicted graphically? A. Square B. Bell C. Triangle D. Star E. Hat For questions 2 through 4, consider the following array of numbers: 5 6 7 7 7 8 8 9 9 9 10 15 19 20 21 2. In the array provided, what is the mode? A. 7 B. 9 C. 10 D. 15 E. Both A and B 3. In the array provided, what is the median? A. 7 B. 9 C. 10 D. 15 E. Both A and B 4. In the array provided, what is the mean? A. 7 B. 9 C. 10 D. 15 E. Both A and B 5. The difference between the smallest and the largest values in a distribution is the _____. A. mean B. median C. mode D. range E. deviation 6. Which of the following is a bar chart arranged in increasing order by size? A. Control chart B. Simple bar chart C. Pareto diagram D. Histogram 7. Which of the following hypotheses is a null hypothesis? A. There is no difference in the monthly grocery bills of families with one child and families with two children B. Grocery bills vary according to the number of meals eaten outside the home C. Families with two children have...

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...Hypothesis Testing Can You Ever Know the Population Standard Deviation? USING STATISTICS @ Oxford Cereals, Part II Fundamentals of Hypothesis-Testing Methodology The Null and Alternative Hypotheses The Critical Value of the Test Statistic Regions of Rejection and Nonrejection Risks in Decision Making Using Hypothesis Testing Hypothesis Testing Using the Critical Value Approach Hypothesis Testing Using the p-Value Approach 9.4 Z Test of Hypothesis for the Proportion The Critical Value Approach The p-Value Approach Potential HypothesisTesting Pitfalls and Ethical Issues 9.5 9.2 t Test of Hypothesis for the Mean (S Unknown) The Critical Value Approach The p-Value Approach Checking the Normality Assumption One-Tail Tests The Critical Value Approach The p-Value Approach 9.6 Online Topic: The Power of a Test USING STATISTICS @ Oxford Cereals, Part II Revisited CHAPTER 9 EXCEL GUIDE CHAPTER 9 MINITAB GUIDE 9.3 Learning Objectives In this chapter, you learn: • The basic principles of hypothesis testing • How to use hypothesis testing to test a mean or proportion • The assumptions of each hypothesis-testing procedure, how to evaluate them, and the consequences if they are seriously violated • How to avoid the pitfalls involved in hypothesis testing • Ethical issues involved in hypothesis testing U S I N G S TAT I S T I C S @ Oxford Cereals, Part II s in Chapter 7, you again find yourself as plant operations manager for Oxford Cereals. You are responsible...

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...whether the data support her belief. • What is the null hypothesis for this test? H0: the reject rate in the packing line for bottles of equine glucosamine is equal to or greater than 32 units per 1,000. Numerically, we write: H0: u => 32 units/1,000 • In the context of this scenario, what would be the consequences of making a Type I error? A Type I error occurs when we reject H0, when it is true. In this case, a Type I would result from concluding that the reject rate in the packing line is not equal to or greater than 32 units per 1,000, when in reality it is actually equal to or greater than 32 units per 1,000. The consequences, would be that the VP of operations would implement the new process, when in reality it would not reduce the rate. Customers may feel deceived and could impact on revenue. • In the context of this scenario, what would be the consequences of making a Type II error? A Type II error occurs when we do not reject H0 when it is false. In this case, a Type II error would result from concluding that the reject rate in the packing line is equal to or greater than 32 units per 1,000. The consequences of the Type II error would be that the VP of operations would not implement the new process, when in fact it improves the process. The company would not be advertising an improvement in process. Scenario 2 Playbill Magazine had reported that the mean annual household income of its readers is $119,155. The most recent random sample of 80 households...

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...that an outcome of an experience or an event will occur (Cozby, 2009). Probability and significance are one in the same. For instance if the statistical significance is low then the difference will be counted as a random error, whereas if it is high it will not. If the significance is low then the probability is considered sound. 3. Explain the relationship between the alpha level (or significance level) and Type I error. What is a Type II error? How are Type I and Type II errors different? (3 points) A significance level α corresponds to a certain value of the test statistic, So the probability of rejecting the null hypothesis when it is true is the probability that t > tα, which is α. In other words, the probability of Type I error is α.1 A Type I error occurs when your reject a true null hypothesis (remember that when the null hypothesis is true you hope to retain it). A Type II error occurs when you fail to reject a false null hypothesis (remember that when the null hypothesis is false you hope to reject it). The best way to allow yourself to set a low alpha level (i.e., to have a small chance of making a Type I error) and to have a good chance of rejecting the null when it is false (i.e., to have a small chance of making a Type...

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...there are two types of errors, which the consortium can make. A Type I Error is referred to as a “false positive.” A Type I error would be made when the null hypothesis is rejected when it should be accepted. This error may occur if the consortium defends any lawsuit against them if they are using 6% (6/100) as their surveying result. The results of the sample size of 100 people indicate that the percentage range is from 1.35% to 10.65%. The test results can be higher than 10%, but actually it is lower. Therefore, if the consortium defends any lawsuit against them it is possible that a Type I Error can be made. The second type of error is a Type II Error, which is also known as “false negative.” A Type II error would be made when the alternative hypothesis is rejected when it should be accepted. For this to occur, the consortium must make a decision to settle the case when the survey result shows a lower percentage than 10% but in reality it is actually higher than 10%. The only error the consortium should make is a Type II error because the alternative hypothesis was rejected. As previously stated, using a sample size of 100 shows that we would not reject the null hypothesis, in other words, this would mean to settle with Tommy. If we did not create a second hypothesis test using a sample size of 300, we would not have defended against Tommy in court and a Type II error would have been made. Size of simple | Defend lawsuit | Settlement | 100 | Type II Error | Right decision...

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... Lall 20 OCTOBER 2014 HYPOTHESIS TESTING AND TYPE ERRORS Answer the following problems showing your work and explaining (or analyzing) your results. 1. Explain Type I and Type II errors. Use an example if needed. Type I errors, also known as an error of the first kind involves the rejection of a true null hypothesis that is actually the equivalent to a false positive. If the null hypothesis is rejected, a statement can be made that the control does in fact have some effect on the test. But if the null hypothesis is true, then in reality the control does not fight the test in any way visible. Although, type I errors can be controlled, the value of alpha is related to the level of importance that are selected as a direct bearing on type I errors. Alpha is the maximum probability that there will be a type I error. If the value of alpha is 0.05 this equates to a 95% confidence level. Meaning there is a 5% probability that a true null hypothesis will be excluded. In the long run, one out of every twenty hypothesis tests performed at this level will result in a type I error. (www.statistics.about.com, 2014). Type II error, also known as a "false negative": the error of not rejecting a null hypothesis when the alternative hypothesis is the true state of nature. In other words, this is the error of failing to accept an alternative hypothesis when you don't have adequate power...

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...“Pizzazz.” Thirty (n=30) random selected Pizzazzes are driven for a month and the mileage is carefully measured in each. The mean mileage for the sample is 28.6 miles per gallon (mpg) and the sample standard deviation is 2.2 mpg. Estimate a 95% confidence interval for the mean mpg in the entire population of Pizzazzes (you might need to round your answer a little bit to agree with mine). (a) (b) (c) (d) (e) (23.42, 33.84) (27.81, 29.39) (26.82, 30.47) (27.23, 30.03) None of the above 2. Determine the test statistic for testing the null hypothesis that the population mean is 27 mpg ( H0 : µ = 27 Ha : µ ≠ 27 ) (a) (b) (c) (d) (e) (f) t = 3.98 t = -3.98 t = 4.6 t = -4.6 t = 1.96 None of the above 3. A Type II error is made when a. b. c. d. e. the null hypothesis is accepted when it is false. the null hypothesis is rejected when it is true. the alternate hypothesis is accepted when it is false. the null hypothesis is accepted when it is true. the alternate hypothesis is accepted when it is true. 4. A recent USA TODAY/CNN/Gallup Poll showed that most American people support Bush’s efforts in the Middle East peace process. The poll of 2000 adults was conducted and 1243 people said they supported Bush’s efforts. a) Find a 95% confidence interval for p, the fraction of Americans who support Bush’s efforts phat = 1243/2000 =62.15% then use the CI formula for a proportion b) Perform the hypothesis test Ho : p = 0.6 versus Ha : p >...

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...INTRODUCTION In the town of Lexington, Massachusetts, the real estate company VALMAX has received many complaints from two sets of customers: the first set believes that they were advised to post asking-prices for their houses that were too low compared to other brokers’ listings while the second set believes that they were advised to accept selling-prices for houses that they purchased that were too high relative to the selling-prices for houses brokered by other realtors. Based on the given data for both VALMAX and the other brokers (will henceforth be called “OTHERS”), it is decided that the clients’ complaints are justified. In order to properly come up with this conclusion, the correct data must first be chosen, the null and alternative hypotheses must be stated, the degrees of freedom will be calculated, the rejection region will be defined, and ultimately, the test statistic will be calculated and interpreted. After this, there are three methods for coming up with the end conclusion, the first being qualitative and the last two being quantitative. ANALYSIS Choosing the Data: Three sets of data are given for both VALMAX and OTHERS for which we assume to be normally distributed: asking prices, selling prices, and the differences between the two. Either the asking/selling prices can be used or the differences data can be used, but not both. The reason why we have chosen to not use the asking and selling price data is because we cannot distinguish between the buying...

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...variables. In this paper, Team C will explain the steps in researching a hypothesis; illustrate a comparison between the means of two or more groups, and make a calculation of the correlation between two variables. We will also reflect on the topics in week four that we are most comfortable with and the topics we struggled with at the same time. Additionally, we will explain how the topics relate to the applications within our personal or professional fields. Steps in Research Hypothesis In science class as children we were taught that a hypothesis was an educated guess, as we blossom into a more mature age we discover that it goes a bit deeper. A hypothesis can be used in different ways most of them in our daily lives. There are two types of statistical test you can perform. The null hypothesis’s that which represents the status quo to the party performing the sampling experiment—the hypothesis that will be accepted unless the data provide convincing evidence that it is false. The alternative, or research, hypothesis is that which will be accepted only if the data provide convincing evidence of its truth. In statistic, there are seven steps you need to perform to arrive at a statistical hypothesis. The first step is the null hypothesis in which you must state a fact until it is proven to be false. The alternative hypothesis is a rejection of the null hypothesis in which you have to prove it is false. The next is the statistic test or the set test, this test is a formula...

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...appropriately large--meaning that you have a higher chance of rejecting the hypothesis that the drug is safe when it fact actually is. Although it shouldn't be too large since you don't want to send to waste a good product. This would give less room for type II error, which would mean you would accept the null hypothesis when if fact it is false. They don't want to say a drug is safe and effective when it actually isn't. Part B Type I error means that you reject the null hypothesis when it is true. Therefore for Set 1, you reject that the drug is safe when it actually is. And for Set 2 you reject that a drug is effective when it actually is. For each of these sets, a type I error would be of concern because you'd actually waste a good profitable product due to bad statistics. Part C Type II error means that you accept the null hypothesis when it is false. For set 1 you would accept that the drug is safe when it actually isn't. For Set 2 you would accept that a drug is effective when it actually isn't For set 1, accepting safety for a drug that could be dangerous, can lead to injury death and subsequently law suits. That's unethical and costly. A type 2 error could ruin the company's reputation. For Set 2, accepting efficacy when it isn't not good for business, because doctor's would quickly stop prescribing your drug or if it is an over the counter, people would stop buying it. It would be a big waste of money, but something...

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...risk factors for development of pneumonia in intensive care unit (ICU)-treated trauma patients (Hyllienmark, Brattstrom, Larsson, Martling, Petersson, & Oldner, 2013). The study consisted of 322 trauma patients submitted to a level one trauma center following initial resuscitation. The study looked at hospital interventions in the first 24 hours after patient was admitted and the possible association with the patient developing pneumonia within 10 days of ICU admission (Hyllienmark et al., 2013). The study “High Incidence of post-Injury pneumonia in intensive care-treated trauma patients” is quantitative in nature it looks at the numerical data collected concerning the topic of pneumonia and ICU admitted patients. This is the article that I will use to incorporate into my paper. Define reliability and validity; explain concurrent and predictive validity. Although reliability must be considered in relation to validity they are both defined in different ways. Reliability can be defined as the obtainment of consistent measurements over time (Schmidt & Brown, 2012). Validity of a study can be defined as the degree to which an instrument measures what it is supposed to measure (Schmidt & Brown, 2012). Validity is broken down into internal and external validity. Internal looks reviews if the independent variable has an effect on the dependent variable. In contrast, external looks to see if the results generated from the study can be generalized to other settings and times...

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...Notes for Statistics 3011 University of Minnesota Fall 2012 Section 010 Instructor: Shanshan Ding Notes accompany the Third Edition of Statistics: The Art and Science of Learning From Data by Alan Agresti and Christine Franklin Contents CHAPTER 9: HYPOTHESIS TESTS 9.1 Elements of a Hypothesis Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Normal Hypothesis Test for Population Proportion p . . . . . . . . . . . . . . . . . . 9.3 The t-Test: Hypothesis Testing for Population Mean µ . . . . . . . . . . . . . . . . . 9.4 Possible Errors in Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5 Limitations and Common Misinterpretations of Hypothesis Testing . . . . . . . . . . 1 1 6 10 15 17 Stat 3011 Chapter 9 CHAPTER 9: HYPOTHESIS TESTS Motivating Example A diet pill company advertises that at least 75% of its customers lose 10 pounds or more within 2 weeks. You suspect the company of falsely advertising the beneﬁts of taking their pills. Suppose you take a sample of 100 product users and ﬁnd that only 5% have lost at least 10 pounds. Is this enough to prove your claim? What about if 72% had lost at least 10 pounds? Goal: 9.1 Elements of a Hypothesis Test 1. Assumptions 2. Hypotheses Each hypothesis test has two hypotheses about the population: Null Hypothesis (H0 ): Alternative Hypothesis (Ha ): 1 Stat 3011 Chapter 9 Diet Pill Example: Let p = true proportion of diet pill customers that lose at least...

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