According to the US Department of Agriculture 588 of males b

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 found that 36 of them consume the recommended daily allowance of calcium.

a) Construct a 99% confidence interval for the above data. Show your work using the formulas.

b) At the = 0.01, 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? Conduct a full hypothesis test by following the steps below.

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).

c) Explain the connection between the confidence interval and the hypothesis test in this problem (discuss in relation to the decision made from your hypothesis test).

Solution