In: Statistics and Probability
Read the following scenarios and answer the questions below.
You are a USUSA officer. You and your fellow student body officers have noticed that your events tend to be attended by many freshmen, but not by many seniors. You want to find out whether students tend to decrease liking the events as they progress through their degree. You collected a survey asking 20 students how much they liked the events when they were freshman (in 2014) and when those same students were seniors (currently).
You are a gastroenterologist who has read that increasing “gut bacteria” leads to improvements in cognitive function. There is very little evidence supporting this statement, so you decide that you would like to conduct your own study to determine whether increasing “gut bacteria” leads to improvements in cognitive function. You conduct an experiment in which one group of participants receive a probiotic (good “gut bacteria”) supplement and another group receive a placebo. After 6 weeks of taking the supplements, you measure participants’ cognitive functioning on a scale from 1 to 50 (1 = worst cognitive function of my life – 50 best cognitive function in my life).
You are a developmental psychologist interested in the development of language in young children. You have created a new toy for infants to increase the speed of learning words. The standard number of words that children can speak at age two is 50. You treat this as the population mean (μ = 50) that you are going to see if your new toy can increase acquisition of words such that μ = 50.
You are an applied behavior analyst interested in a new program for increasing treatment integrity (i.e., increasing the reliability of the treatment) for children with Autism who engage in problem behavior. At your clinic, you make an initial observation of your therapists and rate their level of treatment integrity on a scale from 1 to 10 (1 = failing to deliver appropriate treatment – 10 = delivering the treatment perfectly). After your initial observation, you implement the new treatment integrity program and conduct another series of observations on the same therapists to determine whether the treatment is successful.
You are a health psychologist interested in the effects of healthcare accessibility on individuals’ well-being. You have access to several years of data from a national repository of health statistics that includes Americans’ scores on a measure called the Barriers to Wellness Inventory (BWI). Higher scores indicate greater stress related to difficulty accessing healthcare. You want to know whether Americans are more or less stressed about barriers to accessing healthcare today than six years ago, according to the BWI. You have access to BWI scores obtained from a sample of individuals in 2013 and you obtain another set of scores from a sample of individuals from this year.
Scenario 1:
Paired sample t-test would be appropriate.
Null Hypothesis(H0): Ratings of USUSA-sponsored events do not decrease significantly as students progress through their degree.
Alternative Hypothesis(H1): Ratings of USUSA-sponsored events decrease significantly as students progress through their degree.
Scenario 2:
Independent samples t-test would be appropriate.
NullHypothesis(H0): There is no significant difference in cognitive functioning between the sample of participants who received the probiotic supplement and the sample of participants who received the placebo.
AlternativeHypothesis(H1): There exists a significant difference in cognitive functioning between the sample of participants who received the probiotic supplement and the sample of participants who received the placebo.
Scenario 3:
One sample t-test would be appropriate.
Null Hypothesis:(H0): The new toy does not significantly increase speed of acquiring words relative to the population mean (μ) of 50.
Alternative Hypothesis(H1): The new toy significantly increases speed of acquiring words relative to the population mean (μ) of 50.
Scenario 4:
Paired sample t-test would be appropriate.
Null Hypothesis(H0): There is no significant difference between the ratings of treatment integrity before and after new treatment integrity program.
Alternative Hypothesis(H1): There exists a significant difference between the ratings of treatment integrity before and after new treatment integrity program.
Scenario 5:
Independent samples t-test would be appropriate.
Null Hypothesis(H0): There is no significant difference in accessibility to healthcare between BWI scores collected in 2013 and BWI scores collected in 2019
Alternative Hypothesis(H1): There exists a significant difference in accessibility to healthcare between BWI scores collected in 2013 and BWI scores collected in 2019.