Question

In: Statistics and Probability

For each situation below, if appropriate, identify the population, the sample, p and p in words,...

For each situation below, if appropriate, identify the population, the sample, p and p in words, and the value of p. Would you trust a confidence interval for the true proportion based on these data? In other words, are all of the assumptions for a one-proportion z-interval met? Explain.

As concert goers enter a stadium, a security guard randomly inspects their backpacks for alcoholic beverages. Of 130 backpacks checked so far, 17 contained alcoholic beverages of some kind. The guards want to estimate the percentage of all backpacks of concert goers at this concert that contain alcoholic beverages.
The website of the English newspaper The Guardian asked visitors to the site to say whether they approved of the recent “bossnapping” actions by British workers who were outraged over being fired. Of those who responded, 49.2% said “Yes. Desperate times, desperate measures.”
An airline wants to know the weight of carry-on baggage that customers take on their international routes, so they take a random sample of 50 bags and find that the average weight is 17.3 pounds.

Expert Solution

1:

Population; All backpacks of concert goers at the given concert

p: True proportion of all backpacks of concert goers at the given concert that contain alcoholic beverages

Sample : 130 selected backpacks

p-hat: Sample proportion of 130 backpacks of concert goers at the given concert that contain alcoholic beverages.It is equal to

Since number of success and failures are greater than 10 and it is given that sample is random sample so conditions for confidence interval has been fulfilled.

2:

Population; All visitors to the site

p: True proportion of all visitors to the site who said yes

Sample : Visitors who responded

p-hat: Sample proportion of visitors to the site who said yes. It is equal to

Sample is not random sample and sample size is not given. So we cannot find whether number of success and failures are greater than 10 or not. So conditions for confidence interval do not fulfill.

3:

Population; All customers of international routes of given airlines

: True average weight of baggage of customers of international routes of given airlines

Sample : 50 selected customer

Sample is random sample and sample size is greater than 50. So conditions for confidence interval fulfilled.

orchestra answered 2 years ago

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