t is believed that 12% of Americans use a traditional antenna to watch network television.  How large a sample is needed to estimate the true proportion that use antennas with 95% confidence and within 2 percentage points? Show all work leading up to your answer below.

please do the following parts, this is one question! hypotheses, assumptions, and please check the assumptions (listed as a problem in the image)

According to a report on consumer fraud and identity theft, 22% of all complaints for a year were for identity theft. In that year, Wisconsin had 787 complaints of identity theft out of 3498 consumer complaints. Does this data provide enough evidence to show that Wisconsin had a higher proportion of identity theft than 22%? Test at the 1% level. State the hypotheses. Ho: p? v Ha: p|? v Calculate the test statistic. Round to four decimal places. Calculate the standardized test statistic. Round to three decimal places. Z = Find the p-value. Round to four decimal places. p-value = State your decision. O Since the p-value is less than .01, reject Họ. O Since the p-value is greater than .01, reject Ho. O Since the p-value is less than .01, fail to reject Ho. O Since the p-value is greater than .01, fail to reject Ho. Interpret the results. O At the 1% level of significance, there is enough evidence to show that the proportion of complaints due to identity theft in Wisconsin is not equal to…

what sample size should a researcher take if he wants to estimate a population proportion to be 2% of the true value with 90% confidence