Which of the following is an example of a paired

Which of the following is an example of a paired design?

A. A teacher taught one class a lesson using technology and another class without technology. Their scores on a quiz were then compared.

B. A teacher taught a lesson using technology and then compared the class scores on a quiz to the national average score.

C. A teacher teaches a lesson using technology and then gives her students a pair of quizzes and compares these results to those from her class the previous year.

D. Pairs of students were matched by similar IQs. One of the pair was taught a lesson using technology and one without technology. Their scores on a quiz were then compared.

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In Exploration 8.1 you used the MAD statistic to evaluate

In Exploration 8.1 you used the MAD statistic to evaluate the strength of evidence for association between the way a question was asked and whether or not someone chose to be an organ donor.

a. Complete a test of significance to determine if there is an association between survey type and whether or not someone chose to become an organ donor using p̂max – p̂min as the statistic. Make sure you give the hypotheses, your p-value, and a conclusion.

b. Compare and contrast the null distribution you found with the p̂max – p̂min statistic vs. the MAD statistic.

c. Compare and contrast the strength of evidence using p̂max – p̂min vs. MAD on this data set.

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State the research question.Researchers from the University of California, Berkeley

State the research question.

Researchers from the University of California, Berkeley wondered whether upper-class individuals behave more unethically than lower-class individuals. To further investigate this question, they studied behaviors of drivers in different makes and models of cars. The cars were a surrogate measure for the drivers’ class status. According to California Vehicle Code, cars must yield to a pedestrian if said pedestrian is crossing within any marked crosswalk. Data were collected from an intersection in the San Francisco Bay Area on three weekdays between 2:00 pm and 5:00 pm in June of 2011. A coder, positioned near the crosswalk, rated the approaching car on a scale from 1 to 5 based on make, age, and physical appearance of the car. The lowest status received a code of 1 and the highest status a code of 5. The coder also recorded whether or not the approaching car yielded to the pedestrian (a confederate of the study) waiting to cross. There were 152 drivers who were scored.

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In Example 8.1 you used the MAD statistic to evaluate

In Example 8.1 you used the MAD statistic to evaluate the strength of evidence for association between the order in which a car arrived at an intersection and whether or not it came to a complete stop.

a. Complete a test of significance to determine if there is an association between order of car and whether or not it came to a complete stop using p̂max – p̂min as the statistic. Make sure you give the hypotheses, your p-value, and a conclusion.

b. Compare and contrast the null distribution you found with the p̂max – p̂min statistic vs. the MAD statistic.

c. Compare and contrast the strength of evidence using p̂max – p̂min vs. MAD on this data set.

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In a study of parents’ perceptions of their children’s size,

In a study of parents’ perceptions of their children’s size, researchers Kaufman etal. (Current Biology, 2013) asked parents to estimate their youngest child’s height. The researchers hypothesized that parents tend to underestimate their youngest child’s size because the youngest child is the baby of the family and everybody else is the family appears bigger compared to the baby. Th e sample of 39 parents who were surveyed underestimated their youngest child’s height by 7.50 cm, on average; the standard deviation for the difference in actual heights and estimated heights was 7.20 cm and the data are not strongly skewed.

a. Which of the following is an appropriate null hypothesis for this study?

A. Parents’ estimate of their youngest child’s height is accurate, on average.

B. Parents tend to overestimate their youngest child’s height, on average.

C. Parents tend to underestimate their youngest child’s height, on average.

b. Which of the following is an appropriate alternative hypothesis for this study?

A. Parents’ estimate of their youngest child’s height is accurate, on average.

B. Parents tend to overestimate their youngest child’s height, on average.

C. Parents tend to underestimate their youngest child’s height, on average.

c. Identify the observational units in this study.

A. Children

B. Parents

C. Actual heights

D. Estimated heights

d. Identify the parameter in this study.

A. The probability that parents will overestimate their youngest child’s height, ????

B. The probability that parents will underestimate their youngest child’s height, ????

C. The probability that parents will correctly estimate their youngest child’s height, ????

D. The average amount by which parents’ guess of their youngest child’s height will diff er from the actual height, ????

e. Explain why the simulation-based method cannot be used to analyze the available information, to investigate whether parents tend to overestimate their youngest child’s height.

f. Explain why a theory-based approach is valid.

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Reconsider the previous exercise about the amount of sleep (in

Reconsider the previous exercise about the amount of sleep (in hours) obtained in the previous night and time to complete a paper and pencil maze (in seconds). Th e equation of the least squares regression line for predicting price from number of pages is time = 190.33 − 7.76 (sleep).

a. Interpret what the slope coefficient means in the context of sleep and time to complete the maze.

b. Interpret the intercept. Is this an example of extrapolation? Why or why not?

Previous exercises

Student researchers asked their subjects how much sleep they had the previous night (in hours) and then timed how long it took them (in seconds) to complete a paper and pencil maze. The results are shown in the scatterplot along with the regression line.

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Reconsider the previous exercise of the study of the Hatha

Reconsider the previous exercise of the study of the Hatha yoga, walking exercise, and wait-list control. Another outcome of interest was change in number of words correctly recalled from a list aft er a time delay. The researchers reported the corresponding p-value to be 0.38. (Note: We have presented a simplified version of the study here.)

a. State the appropriate null and alternative hypotheses in words.

b. State the appropriate null and alternative hypotheses in symbols. Be sure to define the symbols used.

c. Based on the p-value reported by the researchers state an appropriate conclusion in the context of the study. Be sure to comment on statistical significance, causation, and generalization along with how you are making your decision.

d. State the conditions under which the results from the theory-based ANOVA test would be valid.

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Statistics students were surveyed and two of the questions they

Statistics students were surveyed and two of the questions they were asked was what type of cellphone they use (Basic, iPhone, Smart Phone that is not an iPhone) and how much sleep they typically get on a school night in hours to see if there is an association between sleep and type of phone. For the purposes of this exercise, we will consider this sample to be representative of all students at the school. The summary statistics are shown in the following table and the data are shown in the dotplots.

a. Identify the explanatory variable and the response variable in this study.

b. State, in words or symbols, the null and alternative hypotheses.

c. Using the summary statistics given, compute the MAD statistic.

d. A null distribution for this study is shown above. Using the MAD statistic you calculated in part (c), will the p value for this test be large or small? Explain.

e. Does it appear there is an association between type of cell phone used and the amount of sleep students get? If so, can you conclude that the type of cellphone being used is causing the difference in sleep times?

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In a survey of statistics students at Hope College, two

In a survey of statistics students at Hope College, two of the questions asked were their weight (in pounds) and the cost of their last haircut, including any hair treatments (in dollars). Th e data can be found in the file Weight- Haircut. Let’s explore whether or not there is evidence of a strong association between weight and cost of haircuts.

a. State the appropriate null and alternative hypotheses.

b. Conduct a simulation analysis with 1,000 repetitions. What is your p-value?

c. Summarize your conclusion from this simulation analysis. If there is an association, describe if it is positive or negative in the context of the study.

d. Can you conclude a cause and effect between weight and cost of a haircut? Why or why not?

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Researchers in a clinical study collected information from their subjects

Researchers in a clinical study collected information from their subjects at the beginning of the study. Two of the variables were body mass index (BMI) and age. We are interested in seeing if there is an association between BMI and age. The data from the study can be found in the file AgeBMI.

a. State the appropriate null and alternative hypotheses.

b. Conduct a simulation analysis with 1,000 repetitions. What is your p-value?

c. Summarize your conclusion from this simulation analysis. If there is an association, describe if it is positive or negative in the context of the study.

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