Sampling Distribution Of Proportion – Questions With
Solutions
.9629 Right Ans - Suppose that 15% of the 1750 students at a school have
experienced extreme levels of stress during the past month. A high school
newspaper doesn't know this figure, but they are curious what it is, so they
decide to ask a simple random sample of 160 students if they have
experienced extreme levels of stress during the past month. Subsequently,
they find that 10% of the sample replied "yes" to the question.
Assuming the true proportion is 15%, what is the approximate probability
that more than 10% of the sample would report that they experienced
extreme levels of stress during the past month?
.0524 Right Ans - A consulting agency reports that only 30% of a
company's website users can successfully use a certain feature of the website.
Skeptical of this claim, one of the website developers takes a simple random
sample of 150 of the company's approximately 8000 users and tests whether
they can use the feature successfully. The developer finds that 36% of the
sampled users use the feature successfully.
Assuming the agency's 30% claim is correct, what is the approximate
probability that more than 36% of the sample would use the feature
successfully?
.8944 Right Ans - An article written for a magazine claims that 78% of the
magazine's subscribers report eating healthily the previous day. Suppose we
select a simple random sample of 675 of the magazine's approximately 50,000
subscribers to check the accuracy of this claim.
Assuming the article's 78% claim is correct, what is the approximate
probability that less than 80% of the sample would report eating healthily the
previous day?
.6827 Right Ans - The Department of Tourism reported that in May of
2017, approximately 63% of the tourists to the Philippines were from Asia.
They also noted that it was the first time that the Philippines had more than
500,000 tourists in the month of May. Suppose another organization had
taken a simple random sample of 600 of the tourists in that population.
Solutions
.9629 Right Ans - Suppose that 15% of the 1750 students at a school have
experienced extreme levels of stress during the past month. A high school
newspaper doesn't know this figure, but they are curious what it is, so they
decide to ask a simple random sample of 160 students if they have
experienced extreme levels of stress during the past month. Subsequently,
they find that 10% of the sample replied "yes" to the question.
Assuming the true proportion is 15%, what is the approximate probability
that more than 10% of the sample would report that they experienced
extreme levels of stress during the past month?
.0524 Right Ans - A consulting agency reports that only 30% of a
company's website users can successfully use a certain feature of the website.
Skeptical of this claim, one of the website developers takes a simple random
sample of 150 of the company's approximately 8000 users and tests whether
they can use the feature successfully. The developer finds that 36% of the
sampled users use the feature successfully.
Assuming the agency's 30% claim is correct, what is the approximate
probability that more than 36% of the sample would use the feature
successfully?
.8944 Right Ans - An article written for a magazine claims that 78% of the
magazine's subscribers report eating healthily the previous day. Suppose we
select a simple random sample of 675 of the magazine's approximately 50,000
subscribers to check the accuracy of this claim.
Assuming the article's 78% claim is correct, what is the approximate
probability that less than 80% of the sample would report eating healthily the
previous day?
.6827 Right Ans - The Department of Tourism reported that in May of
2017, approximately 63% of the tourists to the Philippines were from Asia.
They also noted that it was the first time that the Philippines had more than
500,000 tourists in the month of May. Suppose another organization had
taken a simple random sample of 600 of the tourists in that population.
