 Statistics Questions

Subject Mathematics Advanced Statistics

Question

1. County officials want to assess the extent of voter support for a proposed bond issue to fund construction of a new wing to a high school. A pilot survey indicated that 80% of the registered voters were in favor of the new addition. You have been asked to perform a follow up with a more extensive survey and would like have a confidence interval of 80% ± 4%. What is your sample size, how did you determine your sample size? Describe the sampling method that you would use draw your sample and why?

2. You have been asked by the county administrator to check the bulk density of the pavement of a newly paved street. The contractor guaranteed a bulk density of 28.3 gr/cc for the asphalt installed on the street. You pulled six random samples with the following bulk densities (29.3, 28.2, 29.1, 28.7, 28.9, and 28.5).

a. Do these data points satisfy the assumptions for inference? Explain.
b. Calculate the mean and standard deviation of the observed bulk densities.
c. Create a 95% confidence interval for the mean bulk densities.
d. Explain the in context what your interval means.
e. Comment on the contractors stated bulk densities of 28.3gr/cc.

3. A report has just been published that states that female students have higher mean grade point averages (GPA) than male students. However, you question the study by stating that larger percentage of male students are enrolled in engineering majors while more female students are enrolled in liberal arts majors. You have the counts of male and female students for both colleges. (Engineering males = 699, Engineering females = 191, Liberal Arts males = 233, Liberal Arts females = 66).
a. State the null and alternative hypothesis.
b. Calculate the expected counts and calculate a Chi Square statistic
c. How many degrees of freedom are in this analysis?
d. State your conclusion with the context of the data and discuss if the distributions for the groups appear to be different.
e. Examine and standardize the residuals and discuss the implications of the finding.

4. Aerobic fitness can be evaluated using a test to measure oxygen uptake while a person runs on a treadmill for a prescribed distance. However, the equipment to measure oxygen uptake is very expensive therefore, only one person can be evaluated at a time. It is much more economical to determine a formula that uses less expensive and simpler methods to evaluate fitness and predict oxygen uptake. In the dataset fitness, measurements of age, weight, runtime, and pulse rates were taken on 31 individuals who ran 1.5 miles. Develop a model to predict oxygen uptake.
a. Write up your equation to predict oxygen uptake.
b. What is the R² of your equation?
c. Provide an interpretation of your equation and describe the method you used to develop your equation.

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