Numerade

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Each of the following functions gives the amount of a substance present at time t. In each case, give the amount present initially (at + = 0), state whether the function represents exponential growth or decay, and give the percent rate. Enter the exact answers. (a) A = 70(1.07)* The initial amount is and it represents < with rate i %. (b) A = 3.02(0.934)* The initial amount is and it represents with rate i %. (c) A = 4000(1.03)' The initial amount is and it represents with rate i %. (d) A = 12(0.89)* The initial amount is and it represents く with rate i %.

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For the following function, find \( f(2) \). \[ f(x)=4 x-x^{2} \] \[ f(2)=\mathrm{i} \]

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A drug company is comparing the results of three medications on the severity of bacillary dysentery in 78 Peace Corps volunteers returning to the US (N = 78). Below are the averages for these three groups. The results are below. By answering the questions below, you will use these data to conduct an F-test (ANOVA) to determine if the groups differ in disease severity. You have been provided with SSB and SStot on an incomplete ANOVA table, to assist you in efficiently completing this problem. Placebo: x̄1 = 16.0, n1 = 26 Ciprofloxacin: x̄2 = 13.0, n2 = 26 Ofloxacin: x̄3 = 13.5, n3 = 26 Complete this F-table F-table Source Sum of Squares df Mean square F-statistic Effect (between) 200 dfb = MSb = F-statistic = Error (within) SSw = dfw = MSw = - Total 715 dftot = - - Using the Critical value F-table, find the corresponding critical F-value for Type I error rate (alpha) of α = 0.05. CV = What do you conclude regarding the null hypothesis? Type either reject or retain into the blank, as one word. Would the p-value be greater or smaller than alpha? Type either greater or smaller into the blank, as one word. What do you conclude about your research question? Do the medications differ in disease severity? Type either same or different into the blank, as one word. Should you do the follow-up t-tests for this ANOVA analysis? Type either yes or no into the blank, as one word. Follow-up Fisher LSD t-tests What is the standard error for all three follow-up t-tests? Using the Critical value t-table, find the corresponding critical T-value for Type I error rate (alpha) of α = 0.05 using Table A-2. CV = +/- What is the t-statistic comparing the placebo to Ciprofloxacin? What do you conclude regarding the null hypothesis? Type either reject or retain into the blank, as one word. In which group is disease severity lower? Type either placebo, Ciprofloxacin, or neither into the blank, as one word . What is the t-statistic comparing the placebo to Ofloxacin? What do you conclude regarding the null hypothesis? Type either reject or retain into the blank, as one word. In which group is disease severity lower? Type either placebo, Ofloxacin, or neither into the blank, as one word . What is the t-statistic comparing the Ciprofloxacin to Ofloxacin? What do you conclude regarding the null hypothesis? Type either reject or retain into the blank, as one word. In which group is disease severity lower? Type either Ciprofloxacin, Ofloxacin, or neither into the blank, as one word .

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Using the most updated dataset above, conduct a dependent (related, paired) samples t-test comparing students’ reported sleep at the beginning of the semester and their sleep now. These variables are labeled Sleep and Sleep2. Report the t-statistic for this analysis: 2.094 Report the two-sided p-value for this analysis 0.041 Is this p-value bigger or smaller than .05 (alpha)? Type either bigger or smaller into the blank, as one word. Report the 95% Confidence interval, as it appears in the output: 95% CI: lower 0.028 , 1.260 upper Is the null value within this interval? Type either yes or no into the blank, as one word. What do you conclude regarding the null hypothesis? Type either reject or retain into the blank, as one word. What do you conclude about your research question? Do students sleep more or less mid-semester or the same amount? Type either less, more, or same into the blank, as one word.

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It may be that a new drug improves cardiovascular health. Because it is a new drug, its effects are not known. You would like to determine for yourself whether the drug makes a DIFFERENCE in cardiovascular health. Let's assume you take patients and measure their cardiovascular health at baseline, and then take the same patients and have them all take the new drug for six weeks. You then measure their cardiovascular health again. These are their results for both the pre/post drug readings of cardiovascular health: Data Pre-drug Results: Post-drug Results: Patient 1: 28 Patient 2: 25 Patient 3: 26 Patient 4: 29 Patient 5: 24 Patient 1: 27 Patient 2: 26 Patient 3: 27 Patient 4: 28 Patient 5: 26 For the following two questions, type either equal or not equal into the blanks. Null hypothesis: μd 0 Alternative hypotheses: μd 0 What are the degrees of freedom for your t test? Using the Critical value t-table, find the corresponding critical t-value for Type I error rate (alpha) of α = 0.05. CV = +/-

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Data Pre-drug Results: Post-drug Results: Patient 1: 28 Patient 2: 25 Patient 3: 26 Patient 4: 29 Patient 5: 24 Patient 1: 27 Patient 2: 26 Patient 3: 27 Patient 4: 28 Patient 5: 26 For the following two questions, type either equal or not equal into the blanks. Null hypothesis: μd 0 Alternative hypotheses: μd 0 What are the degrees of freedom for your t test? Using the Critical value t-table, find the corresponding critical t-value for Type I error rate (alpha) of α = 0.05. CV = +/- T-statistic What is the sample size? Difference scores for the patients Remember to subtract the Time 2 score from the Time 1 score and include a negative sign, when relevant: Patient 1: Patient 2: Patient 3: Patient 4: Patient 5: Sum of the difference scores: Mean of the difference scores (dbar). Remember to include a negative sign, if relevant. Standard Deviation of the Difference Scores Calculate the deviation scores and then enter the squared deviation scores for the patients below: Patient 1: Patient 2: Patient 3: Patient 4: Patient 5: Sum of squares: Variance of the difference scores: Standard deviation of the difference scores: What is the standard error: What is the unstandardized effect in this problem? Remember to include a negative sign, if relevant: Observed t-statistic. Remember to include a negative sign, if relevant: Confidence Interval and Effect size: Calculate the 95% Confidence interval. Remember to include a negative sign, if relevant. 95% CI: lower , upper Does this interval contain the null value? Type either yes or no into the blank, as one word. Calculate the standardized effect size (Cohen's d). What is the size of this effect. Type either small, medium, or large into the blank, as one word. Conclusions What do you conclude regarding the null hypothesis? Type either reject or retain into the blank, as one word. Would the p-value be greater or smaller than alpha? Type either greater or smaller into the blank, as one word. What do you conclude about your research question? What is the drug's effect on health? Is health higher, lower, or the same among patients, after they take the drug? Type either higher, lower, or same into the blank, as one word.

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What is the relationship between a chosen level of confidence for a confidence interval and how wide that interval is? For instance, if you move from a 95% CI to a 90% CI, what happens? Hint: look at the t-table to see how critical values change when you change levels of significance. Group of answer choices The lower the confidence, the more narrow the interval, and thus the less likely it is you will reject the null. The lower the confidence, the more narrow the interval, and thus the more likely it is you will reject the null. The lower the confidence, the wider the interval, and thus the more likely it is you will reject the null. The lower the confidence, the wider the interval, and thus the less likely it is you will reject the null.

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What does a confidence interval represent? Group of answer choices All of the other answers are true. A way to determine the margin of error for a parameter estimate. A range of possible parameter values, we have some level of confidence the real parameter may fall between. A way to decide if we should reject the null hypothesis.

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Please include at least two places after the decimal point for all answers. Answer numerical questions as numbers (1, 2), not words (one, two). It may be that sunshine has a unique effect on learning statistics. Previous research has been in disagreement, with some studies showing that sunshine increases amount learned whereas others show sunshine has detrimental effects on learning. You would like to determine for yourself whether or not sunshine makes a DIFFERENCE on statistics learning. Let's assume you take five statistics students and give them a lesson on a sunny day, and then take a completely different and unrelated five students and give them the same lesson on a rainy day. These are their results for a quiz on their lesson: Sunny Day Students: Student 1: 21 Student 2: 18 Student 3: 19 Student 4: 21 Student 5: 17 Rainy Day Students: Student 6: 20 Student 7: 18 Student 8: 18 Student 9: 21 Student 10: 20 Please answer the following questions using the information above. What is the mean for the sunny day students? What is the variance of the sunny day students? What is the standard deviation of the sunny day students? What is the mean of the rainy day students? What is the variance of the rainy day students? What is the standard deviation of the rainy day students? What is the pooled variance? What is the unstandardized effect? What is the standard error? What is the t-statistic? What is Cohen's D? Please only report the absolute value of D (a positive number). Conclusions Using the Critical value t-table, find the corresponding critical z-value(s) for Type I error rate (alpha) of α = 0.05 Should you reject or retain the null? Type either reject or retain as one word. Would the p-value be smaller or larger than alpha? Type either smaller or larger as one word. Is the sunny day learning higher, lower, or the same compared to the rainy day students? Type either higher, lower, or same as one word.

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Please answer the following questions using the information below: A random sample of 16 undergraduate political science majors answered questions on a political orientation questionnaire that measures liberalism. Here is their data: x̄ = 54.157 Sx = 8.220. In the general population, scores on this questionnaire are normally distributed with a mean (μ) of 49. You hypothesize that this sample is not representative of the general population. Specifically, you hypothesize that political science students form a distinct sub-population, with DIFFERENT liberalism, relative to the general population. That is, it would be equally interesting to find out they have higher or lower liberalism. Conduct a one-sample t-test by answering the following questions. The null hypothesis is The alternative hypothesis is Are you going to be using a one- or two-tailed test? What are the degrees of freedom for this test? Calculate your observed t-statistic. Using the Critical value t-table, find the corresponding critical t-value(s) for Type I error rate (alpha) of α = 0.05. Calculate the confidence interval. What do you conclude regarding the null hypothesis? Calculate Cohen's D. Please only report the absolute value of D (a positive number). What size effect was Cohen's d? In everyday language, what do you conclude about your research question?

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jamie f.