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Various concepts related to hypothesis testing and confidence intervals, including the interpretation of p-values, null and alternative hypotheses, significance levels, and the relationship between confidence intervals and hypothesis tests. It discusses topics such as comparing proportions, testing means, and evaluating associations between variables. Explanations and examples to help understand the underlying statistical principles and the appropriate application of these techniques. By studying this document, students can gain a deeper understanding of the fundamental statistical methods used in data analysis and decision-making.

Typology: Exams

2023/2024

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Download Hypothesis Testing and Confidence Intervals and more Exams Mathematics in PDF only on Docsity! MATH 210 Review Exam Questions with 100% Correct Answers 2024. After you conduct a coin-flipping simulation, a graph of the ___________ will be centered very close to 0.5. (Check all that apply) A. process probability B. sample size C. proportion of heads D. number of heads E. none of these - Correct answer C. proportion of heads The graph of a null distribution will be centered approximately on ___________. (Check all that apply) A. the observed proportion B. the value of the probability in the null hypothesis C. the number of repetitions performed D. the observed count E. none of these - Correct answer B. the value of the probability in the null hypothesis The p-value of a test of significance is ___________. (Check all that apply) A. the probability the alternative hypothesis is true B. the probability the null hypothesis is true C. the probability, assuming the alternative hypothesis is true, that we would get a result as extreme as the one that was actually observed D. the probability, assuming the null hypothesis is true, that we would get a result as extreme as the one that was actually observed E. none of these - Correct answer D. the probability, assuming the null hypothesis is true, that we would get a result as extreme as the one that was actually observed When we get a p-value that is very large, we may conclude that: (Check all that apply) A. There is strong evidence for the alternative hypothesis B. There is strong evidence against the null hypothesis C. The null hypothesis has been proven to be true D. The alternative hypothesis has been proven to be true E. It is plausible that the null hypothesis is true F. The null hypothesis is unlikely to be true G. None of these - Correct answer E. It is plausible that the null hypothesis is true When we get a p-value that is very small, we may conclude that: (Check all that apply) A. There is strong evidence against the null hypothesis B. There is strong evidence for the alternative hypothesis C. The alternative hypothesis is unlikely to be true D. The null hypothesis is unlikely to be true Page 1 of 11 E. It is plausible that the null hypothesis is true F. The null hypothesis has been proven to be true G. The alternative hypothesis has been proven to be true H. None of these - Correct answer A. There is strong evidence against the null hypothesis B. There is strong evidence for the alternative hypothesis D. The null hypothesis is unlikely to be true Suppose that a standardized statistic (standardized sample proportion) for a study is calculated to be 3.5. Which of the following is the most appropriate interpretation of this standardized statistic? A. The observed value of the sample proportion is 3.5 times the hypothesized parameter value. B. The observed value of the sample proportion is 3.5 SDs above the hypothesized parameter value. C. The study results are statistically significant. D. The observed value of the sample proportion is 3.5 SDs away from the hypothesized parameter value. E. None of these. - Correct answer B. The observed value of the sample proportion is 3.5 SDs above the hypothesized parameter value. When stating null and alternative hypotheses, the hypotheses are A. Sometimes about the statistic and sometimes about the parameter B. Always about both the statistic and the parameter C. Always about the statistic only D. Always about the parameter only E. None of the above. - Correct answer D. always about the parameter only When using simulation or theory-based methods to test hypotheses about a proportion, the process of computing a p-value is A. the same if the sample is from a process instead of from a finite population B. different if the sample is from a process instead of from a finite population C. sometimes different and sometimes the same if the sample is from a process instead of a finite population D. None of the above. - Correct answer A. the same if the sample is from a process instead of from a finite population The monthly salaries of the 3 people working in a small firm are: $3500, $4000, and $4500. Suppose the firm makes a profit and everyone gets a $100 raise. A. How, if at all, would the average of the 3 salaries change? (Increase, Decrease, stay the same) B. How, if at all, would the standard deviation of the 3 salaries change? (Increase, Decrease, stay the same) - Correct answer A. increase B. stay the same Page 2 of 11 D. Statistical significance and statistical confidence - Correct answer C. The explanatory variable and the response variable Can a study have both random sampling and random assignment? If so, explain what can be determined from such a study if significance is found. A. In this case, researchers can generalize results to the population and can infer cause- and-effect relationships between the explanatory and response variables. B. In this case, researchers can generalize results to the population but cannot infer cause- and-effect relationships between the explanatory and response variables. C. In this case, researchers cannot generalize results to the population and cannot infer cause-and-effect relationships between the explanatory and response variables. D. In this case, researchers cannot generalize results to the population but can infer cause- and-effect relationships between the explanatory and response variables. - Correct answer YES A. In this case, researchers can generalize results to the population and can infer cause- and-effect relationships between the explanatory and response variables. The following do plot gives the ages of 21 male rattlesnakes. If one of the rattlesnakes whose age is given as 13 years is actually 14 and that change is made in the data set, would the following numerical statistics become smaller, stay the same, or become larger? Mean: Median: Standard deviation: Inter-quartile range - Correct answer Mean: LARGER Median: SAME Standard deviation: LARGER Inter-quartile range: SAME PAIRED OR NOT PAIRED A. Test scores for students in a biology class taught by Professor Quick are being compared to test scores in a different section of the biology class taught by Professor Quack. B. Pulse rates for students at the beginning of class are being compared to pulse rates for the same students at the end of class. C. The weights of 10-year olds in 2009 are being compared to the weights of 10-year olds in 1994. - Correct answer A. Not paired B. paired C. Not Paired 1. Is there an association between gender and whether or not a person gets the flu? 2. Is the average human body temperature higher than 98.6 \ {} ^\circa F? Page 5 of 11 3. Is there an association between gender and GPA? 4. Will rats go through a maze faster after given caffeine compared to the same rats without caffeine? ------------------------------------------------------------ A. Comparing two proportions B. Testing a mean difference (paired data) C. Testing a single proportion D. Testing a single mean E. Comparing two means (independent) F. None of the above - Correct answer 1. A 2. D 3. E 4. B Which of the following are true about the MAD statistic? There may be more than one statement that is true (select all that apply). A. the MAD statistic can never be negative. B. the MAD statistic is the average distance sample proportions are from each other. C. As the MAD statistic increases, the p-value decreases. D. the MAD statistic is the average of a group of sample proportions. - Correct answer A. The MAD statistic can never be negative. B. the MAD statistic is the average distance sample proportions are from each other. C. As the MAD statistic increases, the p-value decreases. As observed proportions move farther apart: A. Both the MAD statistic and the p-value will decrease. B. the MAD statistic will decrease and the p-value will increase. C. Both the MAD statistic and the p-value will increase. D. the MAD statistic will increase and the p-value will decrease. - Correct answer D. The MAD statistic will increase and the p-value will decrease. Null distributions using the MAD statistic will be: A. Symmetric and centered at zero. B. Skewed right. C. Skewed left. D. Symmetric and centered at the MAD statistic. - Correct answer B. Skewed right. Alive the differences in population means increase, you will be (MORE or LESS) likely to reject the null hypothesis. Page 6 of 11 B. If the population standard deviations increase, you will be (MORE or LESS) likely to reject the null hypothesis. C. If the significance level increases, you will be (MORE or LESS) likely to reject the null hypothesis. D. If the sample size increases , you will be (MORE or LESS) likely to reject the null hypothesis. - Correct answer A. MORE B. LESS C. MORE D. MORE Which of the following are properties of correlation, r? Select all that apply. A. If the correlation between two quantitative variables is zero, then there is no relationship between these two variables. B. The sign of r tells the direction of the linear relationship between two quantitative variables. C. -1 < r < 1 D. Correlation measures the strength of a linear relationship between two quantitative variables. - Correct answer B. The sign of r tells the direction of the linear relationship between two quantitative variables. C. -1 \led r \led 1 D. Correlation measures the strength of a linear relationship between two quantitative variables. An instructor wanted to investigate whether there was an association between height (inches) and hand span (cm). She collected data from 10 students, and after analyzing the data found the p-value for to be 0.027. Check the box of each true statement. Select all that apply. A. The p-value says that there is a 2.7% probability that there is no association between height and hand span. B. If there were no association between height and hand span, the probability of observing the association observed in the sample data of 10 students is 0.027. C. The p-value says that there is a 2.7% probability that there is an association between height and hand span. D. If there were no association between height and hand span, the probability of observing the association observed in the sample data or an even stronger association in a sample of 10 students is 0.027. E. If there were an association between height and hand spy - Correct answer D. If there were no association between height and hand span, the probability of observing the Page 7 of 11 A. High school students sleep between 0.2 and 0.9 hours longer per night than college students. B. High school students sleep between 0.2 and 0.9 hours longer per night, on average, than college students. C. The probability a high school student sleeps longer than a high school student is between 0.2 and 0.9. D. High school students sleep between 0.2 and 0.9 times longer, on average, than college students. - Correct answer B. High school students sleep between 0.2 and 0.9 hours longer per night, on average, than college students. Suppose you are conducting a test of significance for the weight of Snickers bars. Your hypotheses are: Null: The population mean weight is 16.4 grams. Alternative: The population mean weight is more than 16.4 grams. From your random sample of 40 Snickers bars, you conclude that the mean weight of all Snickers bars is more than 16.4 grams with a p-value of 0.02. Which of the following statements best describes what that p-value means? A. If the mean weight of all Snickers bars is 16.4 grams, the probability that a random sample of 40 Snickers would have a mean as high as or higher than the one we found is 0.02. B. If the mean weight of all Snickers bars is more than 16.4 grams, the probability that a random sample of 40 Snickers would have a mean as high as or higher than the one we found is 0.02. C. The proportion of Snickers bars that have weights more than 16.4 grams is 0.02. D. The probability that the mean weight - Correct answer A. If the mean weight of all Snickers bars is 16.4 grams, the probability that a random sample of 40 Snickers would have a mean as high or higher than the one we found is 0.02. Which of the following is an example of a matched pairs design (dependent samples)? A. A teacher compares the scores of students using a computer based method of instruction with the scores of other students using a traditional method of instruction. B. A teacher compares the pre-test scores for a group of students with post-test scores for the same group of students. C. A teacher compares the scores of students in her class on a standardized test with the national average score. D. A teacher calculates the average of scores of students on a pair of tests and wishes to see if this average is larger than 80%. - Correct answer B. A teacher compares the pre-test scores for a group of students with post-test scores for the same group of students. Page 10 of 11 Suppose we have a collection of the heights of all students at your college. Each of the 250 people taking statistics randomly takes a sample of 40 of these heights and constructs a 95% confidence interval for mean height of all students at the college. Which of the following statements about the confidence intervals is most accurate? A. About 95% of the heights of all students at the college will be contained in these intervals. B. About 95% of the time, a student's sample mean height will be contained in his or her interval. C. About 95% of the intervals will contain the population mean height. D. About 95% of the intervals will be identical. - Correct answer C. About 95% of the intervals will contain the population mean height. Page 11 of 11