In Denmark, the threshold for political parties in elections to the Folketing is 2%. In all of the 5 elections that the party Kristendemokraterne (KD) has participated in under its current name, they have become below this threshold.

A survey is being carried out where a representative sample of Danes are asked of which party they want to vote for in the next Folketingsvalg. 1017 people have answered the survey, and 12 of these answered that they want to vote for KD.

a. Calculate a 99%-confidence interval for the proportion of the Danish population that wants to vote for KD. (Note that the proportions in the interval should be in numbers between 0 and 1, and not in percentage).

b. How large must the sample in the survey have been for the width of the confidence interval to have been 1% or less?

Another Danish party, Liberal Alliance (LA), has come above the threshold in all the Folketingsvalg since its establishment in 2007. In the last Folketingsvalg, LA was close to falling below the threshold, with support of only 2.3%. In the survey described above, 14 people answered that they want to vote for LA.

c. Based on the results from this survey, perform a hypothesis test with a 5% significance level to investigate if LA will fall below the threshold or not in the next Folketingsvalg

A competing survey agency believes that the survey described above is not to trust because it is carried out over the internet. In their survey, they have called a representative sample of Danes to ask which party they are going to vote for in the next Folketingsvalg. They got 248 people to participate in their survey, and 2 of them said that they will vote for LA.

d. Based on the second survey, perform a hypothesis test with a 10% significance level to investigate if LA will fall below the threshold or not.