According to the U.S. Department of Agriculture, 58.8% of males between 20 and 39 years old consume the minimum daily requirement of calcium.
After an aggressive "Got milk" advertising campaign, the USDA conducted a survey of 55 randomly selected males between the ages of 20 and 39 and finds that 36 of them consume the recommended daily allowance of calcium.
a. What is (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (????D (the mean difference from a matched pairs design)????????2 (the mean difference from independent samples); p, or p1 - p2) and describe it in words.
b. Construct a 96% confidence interval for the above data. Interpret the confidence interval as we learned in class. Show your work using the formulas.
c. Construct a 96% confidence interval for the above data using the Plus Four Estimate. Interpret the confidence interval as we learned in class. Show your work using the formulas.
d. At the 0.05 significance level, is there evidence to conclude that the percentage of males between the ages of 20 and 39 who consume the recommended daily allowance of calcium has increased?
i. State the null and alternative hypotheses.
ii. State the significance level for this problem.
iii. Check the conditions that allow you to use the test statistic, and, if appropriate, calculate the test statistic.
iv. Calculate the P-value and include the probability notation statement.
v. State whether you reject or do not reject the null hypothesis.
vi. State your conclusion in context of the problem (i.e. interpret your results).
e. If the true population proportion was 0.588, did you commit an error? If so, which type of error did you commit and why? If not, why not? Answer in complete sentences