# Project #45128 - Stats Homework

1.  TIPS (Teachers involve Parents in Schoolwork) is a program designed to improve the quality of homework assignments for elementary and high school students by involving parents in the homework process.  But does TIPS lead to better understanding of the material?  To investigate, high school students were randomly assigned to either TIPS homework assignments or conventional assignments for a two-month period (the students were enrolled in the same courses (different classes) and the assignments covered the same material).  TIPS vs. conventional assignments were given in science and language arts.  At the end of the two month study period, all students took the same science and language arts exams.  Our primary research question is whether performance on the exams differs for students in the TIPS vs. conventional homework groups.  A secondary question is whether TIPS actually increased parent involvement in homework.

Hypothetical data from 180 high school students are attached with this project.  Variables in the data set are: 1) an id number, ranging from 1 to 180; 2) tips, a variable indicating study group, coded 1 for those who were in the TIPS group and 0 for those in the conventional homework group; 3) grade in school, ranging from 10 to 12; 4) sexf, coded 1 for females and 0 for males; 5) language, the score out of 100 on the language  arts exam; 6) science, the score out of 100 on the science exam; and 7) parentwork, the student’s response to the question ‘Did a parent regularly participate in your homework over the past 2 months?’, coded 1 for ‘yes’ and 0 for ‘no’.

1A.  As a description of the study sample, complete the following table.  You do not need to do any statistical testing (no p-values or confidence intervals are needed).

Comparison of the TIPS and Conventional homework samples.  Give the number and percent of each study group that are 10th graders, 11th graders, male, etc.

 TIPS Homework (n = 86) Conventional Homework (n = 94) Grade    10    11    12 Sex    Male    Female 23 (26.7%) 41 (47.7%) 22 (25.6%)   48 (55.8%) 38 (44.2%) 22 (23.4%) 34 (36.2%) 38 (40.4%)   45 (47.9%) 49 (52.1%)

1B.  Our primary question is whether the TIPS or Conventional homework program lead to better scores on the exams.  Analyze performance on the science and language arts exams separately.  Provide a table summarizing the relevant data from the study                 (don’t just annotate or cut-and-paste computer output – create your own table).  Report on the statistical procedure used, give the value of the test statistic, degrees freedom, p-value, and give an interpretation of your findings.

1C.  As a secondary question, we would like to know whether the TIPS homework program actually increased parent participation in their child’s homework.  What percent of TIPS students reported that their parents regularly participated in their homework?  What percent of students given conventional assignments reported that their parents were involved with homework?  Compare these percentages through an appropriate statistical procedure.  Provide a table summarizing the relevant data (don’t just annotate or cut-and-paste computer output – create your own table).  Report on the statistical procedure used, give the value of the test statistic, degrees freedom, p-value, and give an interpretation of your findings.

2.  A study published in the American Journal of Public Health examined the accuracy of weight loss information found through web searches (Modave et al., Analysis of the Accuracy of Weigh Loss Information Search Engine Results on the Internet, AJPH Oct. 2014).  The ‘subjects’ for these analyses were web sites, and each web site was graded on the accuracy of its weight loss information.  Accuracy scores could range from 0 to 28, with higher values indicating better accuracy.  Web sites were also categorized by type of site, and we are interested in whether the accuracy of weight loss information differs by type of site.  Below is a summary of weight loss accuracy scores for medical/university/government, blog, and commercial sites:

 Type of Web Site Med/Uni/Gov Blog Commercial N Mean Std Dev 14 10.67 3.17 7 10.81 2.35 21 5.92 3.42

2A.  Does the accuracy of weight loss information differ between medical/university/government sites and commercial web sites?  Test through an appropriate procedure.  Report the statistical procedure used, value of the test statistic, degrees of freedom, and two-tailed p-value, and give a summary statement of your results.

Two tailed t-test; t-test=4.167; d.f=33; p=.002 (p-value<.001); Reject the null—Medical/university/government sites are significantly more accurate in weight loss information than in commercial websites.

2B.  (No calculations needed)  To compare the accuracy of weight loss information presented in blogs vs. medical/university/government sites, an investigator calculated the difference in mean accuracy scores for these types of sites (10.81 – 10.67 = 0.14) and the 95% CI for this difference (-2.70 , 2.98).   What can you conclude about the significance of the difference in accuracy between these two types of sites, based on this confidence interval?  Explain.

There is no significant difference in the accuracy between the two types of sites based on the confidence interval because the mean does not equal 0.

3.  A study published in the American Journal of Public Health examined compared smoking behavior among adults with and without mobility impairments (Borrelli et al., Cigarette Smoking among Adults with Mobility Impairment: A US Population-Based Survey, Oct. 2014).  The following summaries are based on this article, although sample sizes have been changed (the article was based on a survey of 32,000 adults) and the analyses simplified a bit.

The following gives the number and percent of current smokers, for those with and without mobility impairments, for respondents between the ages of 21 and 44:

 Mobility Impairment No Mobility Impairment Total n n smoking Percent smoking 150 58 38.7 2000 430 21.5

3A.  Give the 95% confidence interval for the percent of young adults (ages 21 to 44) without mobility impairment who smoke, and give an interpretation of this confidence interval.

(19.7%, 23.3%); We are 95 percent confident that between 19.7 percent and 23.3 percent of young adults without mobility impairment smoke.

3B.  Are young adults with mobility impairment more likely to smoke than young adults without mobility impairment?  Test through an appropriate statistical procedure, reporting the procedure used, the value of the test statistic, degrees of freedom, two-tailed p-value, and give a summary of your conclusion.

Chi square=23.534; d.f.=1; p-value=1.23E-6; Reject the null: those with mobility impairment are significantly more likely to smoke than those without mobility impairment.

3C.  (No calculations necessary)  For older adults (ages 65+), 8.2% of those with mobility impairment smoked, compared to 7.6% of those without mobility impairment.  The p-value comparing these two percentages was p=0.603.  Are older adults with mobility impairment more likely to smoke than older adults without mobility impairment?  Explain.

Because our p-value is greater than .05, we failed to reject the null and conclude that among older adults there is no significant difference between smokers with mobility impairment and those without.

4a.  If calculated on the same set of data, would a 99% confidence interval be wider or narrower than a 95% confidence interval?

Wider.

4b.  A research study focused on comparing means between an intervention and control group, and reported that ‘the mean for Group A was significantly higher than the mean for Group B’ with a 1-tailed p-value of 0.038.  What would the two-tailed p-value be for this study?

.076

4c.  The mean birth weight, in grams, for a sample of n=30 infants, was 3,250 gms, with a standard error of 89 gms.  What is the standard deviation for birth weight in this sample?  What is the difference between the interpretation of the standard error and the standard deviation?

Sd=487.47

Standard error: measures the variability of the mean from sample to sample.

Standard deviation: measures the variability from subject to subject.

 Subject Mathematics Due By (Pacific Time) 10/27/2014 01:30 pm
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