Exam 7: Comparing Two Means

In order to investigate whether talking on cell phones is more distracting than listening to car radios while driving, sixty-four student volunteers (from a single college class) were randomly assigned to a cell phone group or a radio group (32 students were assigned to each group). Each student "drove" a machine that simulated driving situations. While "driving" the simulator, a target would flash red at irregular intervals. Participants were instructed to press the "brake" button as soon as possible when they detected a red light. Participant response times were measured as the time between the red light appearing and pushing the brake button. While driving, the radio group listened to a radio broadcast and the cell phone group carried on a conversation on the cell phone with someone in the next room. The cell phone group had an average response time of 585.2 milliseconds (SD = 89.6), and the control group had an average response time of 533.7 milliseconds (SD = 65.3). -Suppose you would like to use a simulation-based method to randomly shuffle the reaction times between the two groups. What would be the main purpose of this use of random shuffling in this simulation?

In order to investigate whether talking on cell phones is more distracting than listening to car radios while driving, sixty-four student volunteers (from a single college class) were randomly assigned to a cell phone group or a radio group (32 students were assigned to each group). Each student "drove" a machine that simulated driving situations. While "driving" the simulator, a target would flash red at irregular intervals. Participants were instructed to press the "brake" button as soon as possible when they detected a red light. Participant response times were measured as the time between the red light appearing and pushing the brake button. While driving, the radio group listened to a radio broadcast and the cell phone group carried on a conversation on the cell phone with someone in the next room. The cell phone group had an average response time of 585.2 milliseconds (SD = 89.6), and the control group had an average response time of 533.7 milliseconds (SD = 65.3). -Calculate the standardized statistic for the appropriate test of two means.

An article that appeared in the British Medical Journal (2010) presented the results of a randomized experiment conducted by researcher Jeremy Groves, whose objective was to determine whether the weight of his bicycle could affect his travel time to work. On each of 56 days (from mid-January to mid-July 2010), Groves tossed a £1 coin to decide whether he would be biking to work on his carbon frame (lighter) bicycle that weighed 20.9 lbs or on his steel frame (heavier) bicycle that weighed 29.75 lbs. He then recorded the commute time (in minutes) for each trip. Here are the summary statistics for his data: -In terms of investigating whether the lighter carbon frame bike will tend to have a higher or lower mean commute time compared to the heavier steel frame bike, which of the following is the correct alternative hypothesis?

An article that appeared in the British Medical Journal (2010) presented the results of a randomized experiment conducted by researcher Jeremy Groves, whose objective was to determine whether the weight of his bicycle could affect his travel time to work. On each of 56 days (from mid-January to mid-July 2010), Groves tossed a £1 coin to decide whether he would be biking to work on his carbon frame (lighter) bicycle that weighed 20.9 lbs or on his steel frame (heavier) bicycle that weighed 29.75 lbs. He then recorded the commute time (in minutes) for each trip. Here are the summary statistics for his data: -Use the Theory-Based Inference applet to find the theory-based p-value for the appropriate test of two means.

Monthly snowfall (in inches) was measured over several winters in Fort Collins, Colorado. Researchers also recorded whether the measurement was taken in the Early winter (September to December) or Late winter (January to June). Boxplots displaying the distribution of monthly snowfall for each season are below. -Which season has the larger median monthly snowfall?

When newborns are held so that their feet just barely touch the floor, they will make instinctive walking and placing motions. This reflex disappears by about eight weeks. Researchers wanted to know if stimulating this behavior in infants during their first eight weeks of life would lead them to walk at an earlier age compared to infants who do not receive this stimulation. To test this they had twelve infants randomly assigned to two groups. Six infants received stimulation of the walking and placing reflex (active group) and six infants receive equal amounts of gross motor and social stimulation, but did not received stimulation of the walking and placing reflex (passive group). The researchers then compared the infant's age (in months) when they first walked and the results are shown in the following figure. -Which of the following applets would be most appropriate to use, in the context of this study?

Monthly snowfall (in inches) was measured over several winters in Fort Collins, Colorado. Researchers also recorded whether the measurement was taken in the Early winter (September to December) or Late winter (January to June). Boxplots displaying the distribution of monthly snowfall for each season are below. -The shape of the distribution of monthly snowfall measurements for the Early season is

A researcher asked random samples of 50 kindergarten teachers and 50 12th grade teachers how much money they spent out-of-pocket on school supplies in the previous school year, To see if teachers at one grade level spent more than the other. A 95% confidence interval for ?_K ? ?₁₂ is $30 to $50. Based on this result, it is reasonable to conclude that

In order to investigate whether talking on cell phones is more distracting than listening to car radios while driving, sixty-four student volunteers (from a single college class) were randomly assigned to a cell phone group or a radio group (32 students were assigned to each group). Each student "drove" a machine that simulated driving situations. While "driving" the simulator, a target would flash red at irregular intervals. Participants were instructed to press the "brake" button as soon as possible when they detected a red light. Participant response times were measured as the time between the red light appearing and pushing the brake button. While driving, the radio group listened to a radio broadcast and the cell phone group carried on a conversation on the cell phone with someone in the next room. The cell phone group had an average response time of 585.2 milliseconds (SD = 89.6), and the control group had an average response time of 533.7 milliseconds (SD = 65.3). -Describe the parameter of interest in words.

Monthly snowfall (in inches) was measured over several winters in Fort Collins, Colorado. Researchers also recorded whether the measurement was taken in the Early winter (September to December) or Late winter (January to June). Boxplots displaying the distribution of monthly snowfall for each season are below. -For the Early season data, if the largest outlier (with a monthly snowfall of 55 inches) were removed from the data set, the sample mean would

When newborns are held so that their feet just barely touch the floor, they will make instinctive walking and placing motions. This reflex disappears by about eight weeks. Researchers wanted to know if stimulating this behavior in infants during their first eight weeks of life would lead them to walk at an earlier age compared to infants who do not receive this stimulation. To test this they had twelve infants randomly assigned to two groups. Six infants received stimulation of the walking and placing reflex (active group) and six infants receive equal amounts of gross motor and social stimulation, but did not received stimulation of the walking and placing reflex (passive group). The researchers then compared the infant's age (in months) when they first walked and the results are shown in the following figure. -State the null and alternative hypotheses for this research question, where 1 = Active and 2 = Passive.

Monthly snowfall (in inches) was measured over several winters in Fort Collins, Colorado. Researchers also recorded whether the measurement was taken in the Early winter (September to December) or Late winter (January to June). Boxplots displaying the distribution of monthly snowfall for each season are below. -What is the upper quartile (Q₃) of the distribution of monthly snowfall measurements for the Late season (approximately)?

An article that appeared in the British Medical Journal (2010) presented the results of a randomized experiment conducted by researcher Jeremy Groves, whose objective was to determine whether the weight of his bicycle could affect his travel time to work. On each of 56 days (from mid-January to mid-July 2010), Groves tossed a £1 coin to decide whether he would be biking to work on his carbon frame (lighter) bicycle that weighed 20.9 lbs or on his steel frame (heavier) bicycle that weighed 29.75 lbs. He then recorded the commute time (in minutes) for each trip. Here are the summary statistics for his data: -In terms of investigating whether the lighter carbon frame bike will tend to have a higher or lower mean commute time compared to the heavier steel frame bike, which of the following is the correct null hypothesis?

Which of the following plots is not appropriate for a quantitative variable?

An article that appeared in the British Medical Journal (2010) presented the results of a randomized experiment conducted by researcher Jeremy Groves, whose objective was to determine whether the weight of his bicycle could affect his travel time to work. On each of 56 days (from mid-January to mid-July 2010), Groves tossed a £1 coin to decide whether he would be biking to work on his carbon frame (lighter) bicycle that weighed 20.9 lbs or on his steel frame (heavier) bicycle that weighed 29.75 lbs. He then recorded the commute time (in minutes) for each trip. Here are the summary statistics for his data: -Calculate the standardized statistic for the appropriate test of two means (carbon - steel).

In order to investigate whether talking on cell phones is more distracting than listening to car radios while driving, sixty-four student volunteers (from a single college class) were randomly assigned to a cell phone group or a radio group (32 students were assigned to each group). Each student "drove" a machine that simulated driving situations. While "driving" the simulator, a target would flash red at irregular intervals. Participants were instructed to press the "brake" button as soon as possible when they detected a red light. Participant response times were measured as the time between the red light appearing and pushing the brake button. While driving, the radio group listened to a radio broadcast and the cell phone group carried on a conversation on the cell phone with someone in the next room. The cell phone group had an average response time of 585.2 milliseconds (SD = 89.6), and the control group had an average response time of 533.7 milliseconds (SD = 65.3). -Assuming the distribution of response times is not strongly skewed in either sample, in evaluating the relationship between whether talking on a cell phone or listening to the radio and response time, would a theory-based approach be valid?

An article that appeared in the British Medical Journal (2010) presented the results of a randomized experiment conducted by researcher Jeremy Groves, whose objective was to determine whether the weight of his bicycle could affect his travel time to work. On each of 56 days (from mid-January to mid-July 2010), Groves tossed a £1 coin to decide whether he would be biking to work on his carbon frame (lighter) bicycle that weighed 20.9 lbs or on his steel frame (heavier) bicycle that weighed 29.75 lbs. He then recorded the commute time (in minutes) for each trip. Here are the summary statistics for his data: -Under the null hypothesis, what distribution does the test statistic follow?

Do children diagnosed with attention deficit/hyperactivity disorder (ADHD) have smaller brains than children without this condition? Brain scans were completed for 152 children with ADHD and 139 children of similar age without ADHD. The mean brain size for the 152 children with ADHD was 1059.4 mL with a standard deviation of 117.5 mL. The mean brain size for the 139 children of with-out ADHD was 1104.5 mL with a standard deviation of 111.3 mL. -The p-value from a simulation-based hypothesis test for these data is 0.0003. What conclusion can be made based upon this p-value?

A random sample of Hope College students was taken and one of the questions asked was how many hours per week they study. You want to see if there is a difference between males and females in terms of average study time. The sample results are given in the following table. -Assuming the distribution of study times is not strongly skewed for either sample, which approach would be more appropriate for these data: simulation-based or theory-based?

Which of the following data sets has the largest standard deviation?