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

(b)(2pts) For each of the following statements, determine whether is TRUE or FALSE. No explanation is required.

(i) TRUE or FALSE: In part (a), if a 95% confidence interval is constructed, the interval would be wider.

(ii) TRUE or FALSE: If another 600 Kansas residents were sampled at random (in late June 2012), the sample proportion that planned to set off fireworks on July 4th would fall in the interval constructed in part (a) with 90% probability.

(c)(3pts) 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?

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

(i) (2pts) Test statistic:

(ii) (2pts) P-value:

(iii) (1pt) Conclusion:

(e) (2pts) What would be a Type 2 error for the test in the previous part? Please describe it in context.