Calculus and Above

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QUESTION 1 Given a sample with...

QUESTION 1

Given a sample with 5 scores: 4, 6, 8, 10, and y, and the mean of this sample is 6, what is the variance of the sample? (Hint: first find y).QUESTION 2

Given a population mean weight of 150 pounds and a population standard deviation 40 pounds, express an individual weight of 200 pounds as a z-score. (to two decimal places, e.g.: 3.21 or 6.00)QUESTION 3

Find the correlation coefficient for these scores (they are given in the form (x1,y1), (x2,y2) etc): (0,1), (10,3), (4,1), (8,2), (8,3) (express this to 3 decimal places, e.g.: .123 or -.456)QUESTION 4

Use the least squares regression equation to find the predicted Y value for an X value of 5, given: r = .3, SSy=64 , SSx=4 , mean of y= 30, mean of x= 10QUESTION 5

You're going skydiving, because you're awesome. The main parachute has to do two things to keep you alive: release when you pull the cord, (probability of releasing = .9) AND unfold properly (probability of unfolding = .8). Unfolding is independent of releasing. OR, if anything goes wrong, your backup parachute will save you (probability of backup working = .7). The backup parachute only comes into play if the first parachute fails. What is the probability that you survive, i.e. that either your primary OR secondary parachute will work? (Hint: this combines both independent and mutually exclusive events, and the answer will be greater than .9). Give the answer to three decimal places, e.g.: .999QUESTION 6

Does eating vegetables instead of delicious foods affect how long you live? Given a population life expectancy of 75 years with population standard deviation 5 years, What is the z-value for a random sample of 25 vegans who live to an average age of 73? Does this alter life expectancy at a .05 level of significance? Type the z-value in box 1 to two decimal places (e.g. 3.45), and in box 2 type either yes or no (yes if this is statistically significant and you reject the null, no if it is not significant and you fail to reject the null).QUESTION 7

A similar follow-up study is done on a sample of 25 meat-lovers who never eat vegetables, again randomly selected from the same general population (population mean life expectancy = 75, population standard deviation = 5). This new sample of meat-eaters live to an average age of 77. What is the lower limit and upper limit of the 95% confidence interval for the life expectancy of this sample of meat-lovers? Type the lower limit in box 1 and the upper limit in box 2, to two decimal places in each case.QUESTION 8

Is working out every day BETTER than working out every other day but for twice as long? A random sample of 42 people are assigned to two groups of equal size: Group 1 works out every day for one hour, Group 2 works out every other day for two hours, and then after a month they are tested for how many pushups they can do in one minute. Group 1 participants do an average of 43 pushups, Group 2 participants do an average of 32 pushups. Given an estimated standard error of 6 pushups, what is the t-value? Is the Group 1 workout plan statistically significantly BETTER than the Group 2 workout plan, at the .05 level? Give the calculated t-value to two decimal places in box 1, and in box 2 type either yes (if it is statistically significant and you reject the null) or no if it is not significant.QUESTION 9

Does study group size affect test performance? From a large class of students, 12 are selected to study for a test either all alone, with a partner, or with a group of other students. The four students who studied alone scored: 7, 10, 9, and 6; the four students who studied with a partner scored: 8, 8, 9, and 7; and the four students who studied in groups scored: 7, 6, 4, and 3. What is the F-value for this study (type in box 1 to two decimal places), and is there a statistically significant effect of study group size on test performance at the .05 level, based on this data (type yes or no in box 2)?QUESTION 10

Do blondes have more fun? Walking around downtown saturday night, you ask people whether they had a boring time, a good time, or a great time that night, and note their hair color. Out of 80 blondes: 20 had a boring night, 20 had a good night, and 40 had a great night. out of 120 non-blondes: 30 had a boring night, 40 had a good night, and 50 had a great night. What is the chi-square value for this data (type in box 1 to two decimal places) and is there statistically significant relationship between hair color and fun at the .05 level (type yes or no in box 2)?

Given a sample with 5 scores: 4, 6, 8, 10, and y, and the mean of this sample is 6, what is the variance of the sample? (Hint: first find y).QUESTION 2

Given a population mean weight of 150 pounds and a population standard deviation 40 pounds, express an individual weight of 200 pounds as a z-score. (to two decimal places, e.g.: 3.21 or 6.00)QUESTION 3

Find the correlation coefficient for these scores (they are given in the form (x1,y1), (x2,y2) etc): (0,1), (10,3), (4,1), (8,2), (8,3) (express this to 3 decimal places, e.g.: .123 or -.456)QUESTION 4

Use the least squares regression equation to find the predicted Y value for an X value of 5, given: r = .3, SSy=64 , SSx=4 , mean of y= 30, mean of x= 10QUESTION 5

You're going skydiving, because you're awesome. The main parachute has to do two things to keep you alive: release when you pull the cord, (probability of releasing = .9) AND unfold properly (probability of unfolding = .8). Unfolding is independent of releasing. OR, if anything goes wrong, your backup parachute will save you (probability of backup working = .7). The backup parachute only comes into play if the first parachute fails. What is the probability that you survive, i.e. that either your primary OR secondary parachute will work? (Hint: this combines both independent and mutually exclusive events, and the answer will be greater than .9). Give the answer to three decimal places, e.g.: .999QUESTION 6

Does eating vegetables instead of delicious foods affect how long you live? Given a population life expectancy of 75 years with population standard deviation 5 years, What is the z-value for a random sample of 25 vegans who live to an average age of 73? Does this alter life expectancy at a .05 level of significance? Type the z-value in box 1 to two decimal places (e.g. 3.45), and in box 2 type either yes or no (yes if this is statistically significant and you reject the null, no if it is not significant and you fail to reject the null).QUESTION 7

A similar follow-up study is done on a sample of 25 meat-lovers who never eat vegetables, again randomly selected from the same general population (population mean life expectancy = 75, population standard deviation = 5). This new sample of meat-eaters live to an average age of 77. What is the lower limit and upper limit of the 95% confidence interval for the life expectancy of this sample of meat-lovers? Type the lower limit in box 1 and the upper limit in box 2, to two decimal places in each case.QUESTION 8

Is working out every day BETTER than working out every other day but for twice as long? A random sample of 42 people are assigned to two groups of equal size: Group 1 works out every day for one hour, Group 2 works out every other day for two hours, and then after a month they are tested for how many pushups they can do in one minute. Group 1 participants do an average of 43 pushups, Group 2 participants do an average of 32 pushups. Given an estimated standard error of 6 pushups, what is the t-value? Is the Group 1 workout plan statistically significantly BETTER than the Group 2 workout plan, at the .05 level? Give the calculated t-value to two decimal places in box 1, and in box 2 type either yes (if it is statistically significant and you reject the null) or no if it is not significant.QUESTION 9

Does study group size affect test performance? From a large class of students, 12 are selected to study for a test either all alone, with a partner, or with a group of other students. The four students who studied alone scored: 7, 10, 9, and 6; the four students who studied with a partner scored: 8, 8, 9, and 7; and the four students who studied in groups scored: 7, 6, 4, and 3. What is the F-value for this study (type in box 1 to two decimal places), and is there a statistically significant effect of study group size on test performance at the .05 level, based on this data (type yes or no in box 2)?QUESTION 10

Do blondes have more fun? Walking around downtown saturday night, you ask people whether they had a boring time, a good time, or a great time that night, and note their hair color. Out of 80 blondes: 20 had a boring night, 20 had a good night, and 40 had a great night. out of 120 non-blondes: 30 had a boring night, 40 had a good night, and 50 had a great night. What is the chi-square value for this data (type in box 1 to two decimal places) and is there statistically significant relationship between hair color and fun at the .05 level (type yes or no in box 2)?

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