1. An investigator wants to determine if a new program aimed at reducing the overall number of pregnancies in a highly populated area is effective (reducing average births below 6 per household). In order to carry out the investigation, the investigator conducts a SRS of 189 participants in the program and finds the average number of births is 4.7 with a sample standard deviation of 0.9 births.Construct a 95% confidence interval for the average number of births per household in this study. Provide a correct interpretation of your interval.
2. Recently there has been quite a bit of controversy about the lack of definitive knowledge about the adverse side effects associated with hormone based birth control usage. Suppose a researcher is interested in the effects of birth control in women aged 18-25 relevant to blood pressure. The researcher assumes that women in this demographic that are taking hormone based birth control are at risk for increased blood pressure. Assume the following table contains the summary statistics of two SRSs, one from a cohort of women taking hormone based birth control, and one from a cohort of women birth control free.
|
Study Arm
|
Average Systolic Blood Pressure (mmHG)
|
Sample Standard Deviation
|
Sample Size
|
|
Birth Control
|
124
|
6.8
|
246
|
|
No Birth Control
|
116
|
4.3
|
267
|
A) Carry out the appropriate statistical procedure to determine if there is a significant difference in the systolic blood pressure between the two groups of women. Write out your null and alternative hypotheses and interpret your results. (Use an alpha level of 0.05)
B) Construct a 95% confidence interval about your point estimate for the average difference in systolic blood pressure between the two groups of females. Provide an interpretation for your interval.
3. Food deserts have become a particularly hot topic in the public health community as an explanation for a variety of negative health outcomes in disadvantaged areas. A researcher is interested in comparing the average shelf space provided by supermarkets, convenience stores, and corner stores in two different communities in order to address the growing concern for food deserts. Assume the following table reports the summary statistics for shelf space dedicated to fresh fruits and vegetables (meters) from SRSs of a variety of different stores that supply groceries from each community.
|
Community
|
Average Shelf Space for Fresh Fruits and Vegetables (m)
|
Sample Standard Deviation
|
Sample Size
|
|
"Food Desert"
|
13.7
|
2.4
|
12
|
|
Other Community
|
89.4
|
14.6
|
14
|
A) Carry out the appropriate statistical test in order to determine if there is a significant difference in mean shelf space between the two communities at the alpha level of 0.05. Assume all conditions for the test are met. Do not assume equal variances. Write out your null and alternative hypotheses, and correctly interpret your pvalue.
B) Construct a 95% confidence interval for your estimate for the average difference in shelf space provided for fresh fruits and vegetables. Provide an interpretation for your interval.
4. Current data provided by the 2010 census indicates that the prevalence of breast cancer in the US is still on the rise, while the mortality rates have slightly declined over time. A researcher at a local health department conducts an observational study to determine the prevalence in the particular region. The researcher gathers 2,168 participants and confirms 246 cases of breast cancer in her sample.
A) Assuming the census data indicates a national prevalence of 23.5%, conduct a formal statistical test to determine if the prevalence calculated in the researcher's study differs significantly from the national prevalence level at the alpha value of 0.05.
B) Interpret your results from the hypothesis test conducted in part A).