Exam 7: Comparing Two Means

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 standard deviation of a simulated null distribution of 1,000 differences in sample mean brain sizes was 13.4 mL. Use the 2SD method to calculate an approximate 95% confidence interval for the difference in population means (ADHD - Without ADHD). (___(1)___, ___(2)___)

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). -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. -Which of the following sentences correctly interprets the first quartile (Q₁) of the distribution of monthly snowfall measurements for the Early season?

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. -State the appropriate null and alternative hypotheses for this research question, where 1 = ADHD and 2 = Without ADHD.

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. -In evaluating the relationship between whether an infant received stimulation of the walking and placing reflex and the infant's age when they first walked, would a theory-based approach be valid?

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). -In terms of investigating whether talking on cell phones is more distracting than listening to car radios while driving, which of the following is the correct null hypothesis?

The boxplots below display the distribution of maximum speed by type of roller coaster for a data set of 145 roller coasters in the United States. -For steel roller coasters, the interquartile range (IQR) is equal to

The boxplots below display the distribution of maximum speed by type of roller coaster for a data set of 145 roller coasters in the United States. -The boxplots show that 25% of wooden roller coasters in the sample travel faster than

The plot below displays the on-base percentage for all Major League Baseball players who played in at least 15 games during the 2018 MLB season based on the player's position. Positions: 1/2/3B = 1st/2nd/3rd base, C = catcher, C/L/RF = center/left/right field, DH = designated hitter, P = pitcher, SS = short stop On-base percentage = (hits + walks + hit by pitch)/(total plate appearances) -At least 50% of on-base percentages for the pitcher (P) are zero.

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: -Which of the following applets would be most appropriate to use, in the context of this study?

The boxplots below display the distribution of maximum speed by type of roller coaster for a data set of 145 roller coasters in the United States. -For steel roller coasters, if the outlier at 120 was removed, the sample mean would

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 boxplots demonstrate that there is an association between which two variables?

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). -Use the Theory-Based Inference applet to find the theory-based 99% confidence interval for . (___(1)___, ___(2)___)

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 standard deviation of a simulated null distribution of 1,000 differences in sample mean brain sizes was 13.4 mL. Calculate the standardized statistic for a test of two means (ADHD - Without ADHD).

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). -Does your interval from question 40 provide significant statistical evidence that the long-run mean response time differs between the cell phone and radio treatments?

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. -What is the value of the statistic we should use in the 3S strategy?

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: -Assuming the distribution of commute times is not strongly skewed in either sample, in evaluating the relationship between bike type and commute 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: -A 95% confidence interval for the difference in long-run mean commute time between frames (Carbon - Steel) is (-2.39, 3.45) min. How would you interpret this interval?

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. -Which "Scenario" would you choose from the pull-down menu of the Theory-Based Inference applet?

The boxplots below display the distribution of maximum speed by type of roller coaster for a data set of 145 roller coasters in the United States. -Which type of roller coaster has the larger median speed?