- Answers should be typed. Work presented in an appendix will not be accepted. 10 points will be deducted from homework where final answers are presented separately from the work.
- Please use the equation editor in Word to
SHOW ALL YOUR WORK for problems requiring hand calculations (see Canvas
for helpful equation editor shortcuts). You will receive partial credit
for showing the steps along the way. A final answer with no work shown
is not enough for full credit.
- For all questions requiring calculations, use 4 decimal points during computations and round to two decimal points at the LAST step.
- Some hints on making the most of homework as
a learning opportunity:
- You can work in groups or discuss the problems with your classmates, but only in a spirit of learning. Do not simply “cut and paste” from others’ work. Your final submission must be strictly your own, though informed by collaborative group work.
- If you do join a group to work on homework assignments, be sure to try all the homework problems on your own first, before meeting with your group. This way, you will have the opportunity to try to devise solutions on your own, without input from others. Then, when you get together, you can compare approaches
Problem 1
Research suggests that providing students with access to nutritious meals may increase academic performance. To assess this claim, a study was conducted by enrolling students from two districts. Students in District A and District B are comparable in demographic characteristics and baseline measures of academic performance. The only difference between the two districts is that in the 2018-19 school year, District A decided to implement a free school lunch program for all students to ensure all students had access to nutritious meals while District B did not adopt the program. At the end of the year, both districts reported the number of students who passed and failed the state’s annual standardized test. The results are provided below. Assume .
| Passed Test | Failed Test | Total | |
| District A – Free Lunch | 2389 | 159 | 2548 |
| District B – No Free Lunch | 3539 | 1295 | 4834 |
| Total | 5928 | 1454 | 7382 |
- Using the table above, compute one marginal probability, one joint probability, and one conditional probability. Label each probability appropriately and provide a brief one-sentence interpretation of the probability in the context of the study.
- State the null and alternative hypotheses to test the claim that the free lunch program is associated with a higher passing rate on the standardized test. Make sure you define any variables that you use. It is not sufficient to just use Greek letters without defining them!
- Convert the data to the appropriate test statistic and calculate the degrees of freedom.
- Compare the test statistic you computed in c) to the critical value of a known distribution and calculate the corresponding p-value range (based on the Sullivan table). Based on this, will you reject or fail to reject the null hypothesis?
- Interpret your findings in the context of the study using a 5% level of significance.
Problem 2
You are working on a study that aims to evaluate the effect of participation in structured social activities on life satisfaction among adults 65 and older. Based on their responses to a questionnaire about social involvement, participants were divided into two groups: those frequently involved in social activities and those infrequently involved in social activities. Life satisfaction was measured using the Satisfaction with Life Scale (Diener, Emmons, Larsen, & Griffin, 1985), which has scores ranging from 5 (low satisfaction) to 35 (high satisfaction). The data are summarized in the following Stata output (Note: 1 = frequent involvement, 0 = infrequent involvement). Assume .
- What type of test should you use to test if the mean life satisfaction scores differ between the two groups of older adults? Explain your reasoning.
- State the null and alternative hypotheses to test the claim that social involvement has an effect on life satisfaction. Make sure you define any variables that you use. It is not sufficient to just use Greek letters without defining them!
- Convert the data to the appropriate test statistic using the provided Stata output and calculate the degrees of freedom.
- Compare the test statistic you computed in c) to the critical value of a known distribution and calculate the corresponding p-value range (based on the Sullivan table). Based on this, will you reject or fail to reject the null hypothesis?
- Interpret your findings in the context of the study using a 5% level of significance.
- Calculate the 95% confidence interval for the mean difference in life satisfaction scores. Does the confidence interval align with the conclusion you drew from the hypothesis test? Explain why or why not.
Problem 3
One of the physicians in the primary care facility where you work has been accused of not adhering to the facility’s guideline of spending an average of 17 minutes of face-to-face time per patient. The supervisor is concerned that any significant deviation from this guideline will detract from the facility’s ability to efficiently treat patients. Before initiating disciplinary actions, the supervisor has asked you to use a sample of the physician’s past 100 patient visits to determine if the accusations are true. Based on these visits, you construct the following table to represent your data. Assume .
| Face-to-Face Time with Patients |
| Mean per-patient face-time |
| Standard deviation |
- State the null and alternative hypotheses to test the claim that the amount of time the physician spends with each patient is different from 17 minutes. Make sure you define any variables that you use. It is not sufficient to just use Greek letters without defining them!
- Convert the data to the appropriate test statistic and calculate the degrees of freedom.
- Compare the test statistic you computed in b) to the critical value of a known distribution and calculate the corresponding p-value range (based on the Sullivan table). Based on this, will you reject or fail to reject the null hypothesis?
- Interpret your findings in the context of the study using a 5% level of significance.
- Provide the point estimate and calculate the 95% confidence interval for the mean number of minutes the physician spends per patient. Provide an interpretation of the confidence interval.
Problem 4
Researchers are interested in the effects of birth order on IQ. To evaluate this relationship, they enrolled 50 pairs of siblings, 50 first-born children and their 50 second-born siblings, for a total of 100 participants. A standard IQ test was administered to each participant when they were 25 years old. Based on these scores, you construct the following table to represent your data. Assume .
| IQ Score at Age 25 |
- State the null and alternative hypotheses to test the claim that IQ scores differ depending on birth order. Make sure you define any variables that you use. It is not sufficient to just use Greek letters without defining them!
- Convert the data to the appropriate test statistic and calculate the degrees of freedom.
- Compare the test statistic you computed in b) to the critical value of a known distribution and calculate the corresponding p-value range (based on the Sullivan table). Based on this, will you reject or fail to reject the null hypothesis?
- Interpret your findings in the context of the study using a 5% level of significance.
Problem 5
How much time did you spend on this assignment? Please estimate to the nearest half hour (e.g. 6.5 hours).
__________ hour(s)
