Hi Soma,
I'll try to answer these questions one by one:
1) First, the alternative hypothesis states that more than 12% of a population is left-handed, so we can eliminate answers C and D because they make a statement about 23% of the population, which was not part of the hypothesis. Additionally, since we are conducting a hypothesis test with significant threshold of 0.05, and we obtain a p-value of 0.23, we can eliminate answer choice A because that answer is what would we say if we obtained a p-value below the threshold of 0.05, not above it. We have enough information here to say that B is the correct answer!
2) In this test, the company obtains a p-value above the threshold of 0.05, which suggests they are not producing >96% high-quality candy. However, they then obtain information that their candy is actually 98% high-quality. This is an example of a Type-II error, which is when a statistical test suggests we cannot reject the null hypothesis (p value is greater than 0.05) but the null hypothesis is actually false (the high-quality percentage of candy IS actually above 96%)! So the correct answer for this question would be D.
3) This question is exactly the same as Question 2- they fail to reject the null hypothesis when it really should be rejected! So this would be another example of a Type-II error, which leads us to an answer of C.
Great questions, thanks for sharing with us!
