Mini 7_ Hypothesis Testing with Z-statistic

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May 21, 2024

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Mini #7 Hypothesis Testing with Z-statistic (answers in bold) 1. Identify at least one confounding variable that undermines the conclusion drawn in the following fictional study description: Prof. Martin meets with his class more frequently than Prof. Mervin. Prof. Martin was interested in which of two popular statistics textbooks ( Statistics: It Will Change Your Life and Statistics: Bigger, Better, Stronger ) was better for students. Prof. Martin compared the two texts by assigning one text to a section of statistics taught by Prof. Miller at 10:00 AM on MWF and the other text to a section of statistics taught by Prof. Mervin from 7-10 PM on Wednesday evenings. At the end of the term, all students took the same comprehensive test. Students who were assigned Statistics: Bigger, Better, Stronger performed better on the test than did students who were assigned Statistics: It Will Change Your Life . Prof. Martin therefore concluded that the former textbook was the better one. 2. What is the difference between a Type I and a Type II error? Type I error which is a false positive or Type II error which is a false negative. Which kind of error is more likely to be published and why? Type I error would be published because it doesn't show that their hypothesis was rejected. Give an example of each and describe a situation that makes these kinds of errors dangerous. Type I error example would be between guilty or innocent and a jury finds the client guilty when the client is actually innocent. Type II error is when there is a false negative like comparing drugs and both drugs aren't effective. Hypothesis testing z-Statistics 3. Students, N = 97, at Ursuline College took Major Field Test in Psychology (MFTP) and scored a mean of 156.11. The mean of the population of students who took the test is mean 156.5 with a SD of 14.6. Is the score of this group of students statistically different from the population? Conduct all steps of hypothesis testing. Please label each step explicitly and please show ALL work. H 0 :μ= 156.5 H 1 :μ≠ 156.5 df= 96 if t<1.662 or >1.987, reject H 0 otherwise, do not reject H 0 S X = 14.6 ÷ 9.8488578018= 1.4824054 t= 156.11-156.5 ÷ 1.4824054= -0.26308593 t= -0.26308593<1.662 therefore reject H 0 (p<.05)

t= -0.26308593> 1.96 Since the calculated z-score falls within the range of -1.96 to 1.96, we do not have enough evidence to reject the null hypothesis. Therefore, we conclude that there is no statistically significant difference between the mean score of the students. 4. Peggy wants to know if her pack of cookies was statistically different from those of the rest of the class (treat as a population). She found out the average number of chips per cookie this year was 13.82 and the standard deviation for the class was 7.25. She had a pack of 10 cookies which had an average of 9.8 chips per cookie. Conduct all steps of a z test. Please label each step explicitly and please show ALL work. H 0 : μ = 13.82 H 1 : μ ≠ 13.82 df= 9 if <-1.752 or >-1.752 reject H 0 otherwise do not reject H 0 S X = 7.25 t= -0.55448276 t= -0.55448276<1.96 therefore reject H 0 t= 1.752< 1.96 Since the calculated z-score falls within the range of -1.96 to 1.96, we do not have enough evidence to reject the null hypothesis. Therefore, we conclude that there is no statistically significant difference between the mean number of chips per cookie. 5. Mehl (2007) published a study in the journal Science reporting the results of an extensive study of 396 individuals comparing the number of words uttered per day by women. He found that on average women uttered 16,215 words a day. The population mean for words per day uttered was 15, 767 with a standard deviation of 238 words per day. Please label each step explicitly and please show ALL work. H 0 : μ = 15,767 H 1 : μ ≠ 15,767 df= 395 if <37.54 or >37.54 reject H 0 otherwise do not reject H 0 S X = 238 t= 1.8825294

t= 1.8825294< 1.96 therefore reject H 0 t=37.54> 1.96 Since the calculated z-score is greater than the critical z-value, we reject the null hypothesis. Therefore, we conclude that there is a statistically significant difference between the average number of words uttered per day by women. 1. A statement that there is no difference between means is a: A) negative statement. B) null hypothesis. C) research hypothesis. D) positive statement. 2. On April 16, 2007, the BBC news reported the results of a study done by Dr. David Lewis of the Mind Lab in the UK. Dr. Lewis found that eating dark chocolate had longer lasting excitatory effects on the body than did kissing your romantic partner. Based on his statement, it is evident that Dr. Lewis: A) rejected the null hypothesis. B) proved the research hypothesis. C) failed to reject the null hypothesis. D) accepted the research hypothesis. 3. Dr. Spock finds results that match his previous predictions. He claims that he has proven his hypothesis. What should he have said? A) The findings reject the null hypothesis. B) The findings support his hypothesis and it is now accepted. C) The findings do not reject the null hypothesis. D) What he said was correct; he has proven his hypothesis to be true. 4. When hypothesis testing, a conservative approach is to use a ________ rather than a ________. A) two-tailed test; one-tailed test B) one-tailed test; two-tailed test C) null hypothesis; research hypothesis D) research hypothesis; null hypothesis

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