In late June 2012, Survey USA published results of a survey stating that 56% of the 600 randomly sampled Kansas residents planned to set off fireworks on July 4th.

(a) Find a 90% confidence interval for the proportion of Kansas residents planned to set off fireworks on July 4th.

(b) Suppose you are designing another survey of fireworks plans among Kansas residents. You would like for the margin of error to be at most 2% for a 95% confidence interval. How big of a sample size should you choose?

(c)Test whether a majority of Kansas residents planned to set off fireworks on July 4h. In other words, test the hypotheses H₀: p = 0.5 versus H_a: p > 0.5, where p is the proportion of Kansas residents who planned to set off fireworks on July 4th. Report the test-statistic, the p-value, and the conclusion at significance level alpha = 0.01.

(d) What would a type 2 error be in part (c)? Please describe it in context.