Consumption of Saturated Fat: A nutritionist claims that the proportion of females who consume too much saturated fat is lower than the proportion of males who consume too much saturated fat. In interviews with 513 randomly selected females, she determines that 300 consume too much saturated fat. In interviews with 564 randomly selected males, she determines that 391 consume too much saturated fat.

a) Determine whether a lower proportion of females than males consume too much saturated fat at the 0.05 significance level. You must state the hypotheses, determine the test statistic and either the P-value(s) or critical value(s). Finally, you must clearly state your conclusion. Round all answers to two decimal places.

b) Construct a 95% confidence interval for the difference between the two population proportions,

c) Does your confidence interval lead you to the same conclusion as your answer to part (a)? Explain.