For an upcoming election in some county of South Carolina, we wish to determine the minimum sample size required in order to estimate the true percentage of registered Democratic voters. Using a 95% confidence level, answer the following

3. For an upcoming election in some county of South Carolina, we wish to determine the minimum sample size required in order to estimate the true percentage of registered Democratic voters. Using a 95% confidence level, answer the following
a. Find the minimum sample size needed. Assume no prior information is known about the registered voters. Use a margin of error of 5% (or 0.05 as a decimal). Round to the nearest whole number.
b. Find the minimum sample size needed. Assume prior information indicates that roughly 28% of voters are registered Democrats. Use a margin of error of 5% (or 0.05 as a decimal). Round to the nearest whole number.
3. Suppose a study is done to determine if a new drug is effective when compared to a placebo drug. There was a total of 324 subjects where 182 of them received the new drug and the remaining received the placebo drug. Out of the 182 who received the new drug. 72 of them had positive results. Out of the 142 who received the placebo drug, over 80 of them had positive results.
a. Using a 0.10 significance level, test the claim that for the overall population who take the drug, the majority of them will have positive results.
i. State the null and alternative hypothesis
ii. Determine the p-value
iii. State the decision about the null hypothesis
iv. State the conclusion atout the claim
a. Then using this same 0.10 significance level, test the claim that for the overall population who take the placebo drug, the majority of them will have positive results.
i. State the null and alternative hypothesis
ii. Determine the p-value
iii. State the decision about the null hypothesis
iv. State the conclusion about the claim
a. Based on your results from parts a. and b., does the new drug appear to be effective when compared to the placebo drug? Why or why not?
3. Listed below are depths ( in km) of recent earthquakes. Use a 0.05 significance level to test the claim that the overall mean depth of earthquakes is equal to 5.4 km.
i. State the null and alternative hypothesis
ii. Determine the p-value
iii. State the decision about the null hypothesis
iv. State the conclusion about the claim
Earthquake depths = 1.2. 8.9.4.3. 2.5, 3.7.4.2. 7.8. 6.5. 3.2. 6.2

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