Sampling Distribution of Proportion

.8469

A camp accrediting association has 2,400 camps in their association. They claim that 45% of their camps offer specialized programs for individuals with disabilities. Suppose you contact a simple random sample of 200 of the camps and ask them whether they offer specialized programs for individuals with disabilities. Assuming that the association's claim is correct, what is the approximate probability that between 40% and 50% of the camps reply "yes" to your question?

.0524

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?

.0423

A local agricultural cooperative claims that 55% of about 60,000 adults in a county believe that gardening should be part of the school curriculum. However, when you take a simple random sample of 300 of the adults in the county, only 50% say that they believe that gardening should be part of the school curriculum. Assuming that the agricultural cooperative's claim is accurate, what is the approximate probability that less than 50% of the sample would say that they believe that gardening should be part of the school curriculum?

.0572

According to a survey, 63% of the Scottish population has visited woodland in the previous year. Skeptical about this claim, you decide to take a simple random sample of 650 people in this population, and you ask them if they had visited woodland in the previous year. You find that 60% of the sample replied "yes" to your question. Assuming that the original survey's 63% claim is correct, what is the approximate probability that less than 60% of the sample would report that they had visited woodland in the previous year?

.4215

According to the 2011 National Survey of Fishing, Hunting, and Wildlife-Associated Recreation, there were over 71 million wildlife watchers in the US. Of these wildlife watchers, the survey reports that 80% actively observed mammals. Suppose that one of the census workers repeated the survey with a simple random sample of only 500 wildlife watchers that same year. Assuming that the original survey's 80% claim is correct, what is the approximate probability that between 79% and 81% of the 500 sampled wildlife watchers actively observed mammals in 2011?

.0478

An article claimed that only 38% of hotel visitors used the alarm clock provided. A hotel manager wanted to see whether that proportion applied to the hotel where she worked, so she took a random sample of 700 of the approximately 10,000 visitors to the hotel one month and checked whether they used their room alarm clock. Of the sampled visitors, only 35% used the alarm clock. Assuming that the article's 38% claim is also the true proportion for visitors to the hotel, what is the approximate probability that less than 35% of the sample used the alarm clock?

.8944

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?

.0228

Beatriz takes a simple random sample of 350 orders from the more than 5000 total orders to her store and finds that 12% of the sampled orders were returned. Assuming that it is really 9% of all orders to her store which were returned, what is the approximate probability that more than 12% of the sampled orders would have been returned?

.9629

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?

.6827

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. Assuming that the reported 63% claim is accurate, what is the approximate probability that the other organization's results were within 2 percentage points of the Department of Tourism's results?

.0548

The United Kingdom Forestry Commission reports that 43% of the 3.16 million hectares of woodland area in the United Kingdom had certification identifying them as "sustainably managed" in 2016. Suppose an employee took a simple random sample of 400 of the hectares and saw that the records showed that 47% of the sampled hectares had that certification in 2016. Assuming that the Forestry Commission's report is accurate, what is the approximate probability that more than 47% of the sample would have had the certification in 2016?

.8703

The school board claims that 85% of the over 1,600 families with children in their district send their children to public school. Skeptical of this claim, a private school administrator takes a simple random sample of 120 families with children in the district and asks them whether they send their children to public school. Assuming the school board's claim is correct, what is the probability that the administrator's results are within 5 percentage points of the school board's 85% claim?