A simple random sample of 1100 males aged 12 to 17 in the UnitedStates were asked whether they played massive multiplayer onlinerole-playing games (MMORPGs); 775 said that they did. a. We want touse this information to construct a 95% confidence interval toestimate the proportion of all U.S. males aged 12 to 17 who playMMORPGs.
State the parameter our confidence interval will estimate (incontext).
b. State the value of our point estimate (i.e., the statistic,). Round to four decimal places.
c. Identify the conditions that must be met to use thisprocedure and explain how you know that each one has beensatisfied.
d. Find the appropriate critical value () and the standard errorof the sample proportion (). SHOW YOUR WORK! Round the standarderror to four decimal places.
e. Use the formula shown in your notes to get the 95% confidenceinterval by hand. SHOW YOUR WORK! Round to four decimal places.
f. Interpret the confidence interval constructed in part (e) inthe context of the problem.
g. Interpret the confidence level in the context of theproblem.
h. Suppose you wanted to estimate the proportion of 12-to-17year-old males who play MMORPG’s with 95% confidence to have amargin of error within ± 2%. Calculate how large a sample you wouldneed. Use the found in (b). SHOW YOUR WORK! Remember to round yourfinal answer up to the nearest whole number.
i. If you wanted to have a margin of error of ±2% with 99%confidence, would your sample have to be larger, smaller, or thesame size as the sample in part (h)? Explain.
j. Suppose MMORPG.com claims that 65% of all U.S. males aged12-17 play massive multiplayer online role-playing games (MMORPGs).Does your 95% confidence interval support this claim?
k. What is the name of the significance test that can we performto test the claim made?
l. What hypotheses would we use if we wished to conduct atwo-sided test?
m. The only condition that changed from earlier is theSuccess/Failure Condition. You must now verify the expected numberof successes and failures using our null hypothesis value.
n. Now we can proceed with the calculations of the standarddeviation (). SHOW YOUR WORK! Round to four decimal places. Note:Remember to use and in the formula.
o. Calculate the z-score. SHOW YOUR WORK!
p. Use your z-score to calculate the p-value. SHOW YOUR WORK!Hint: Remember to double the p-value if you start by calculating aone-sided probability.
q. Interpret the p-value in context.
r. What decision would you draw based on the size of thep-value?
s. Are our confidence interval and significance test results inagreement?
