From a survey of coworkers, you find that $48 \%$ of 200 have already received this year's flu vaccine. An approximate $95 \%$ confidence interval is $(0.409,0.551)$. Is the following true? If not, describe briefly.

e) We are $95 \%$ confident that between $40.9 \%$ and $55.1 \%$ of the samples will have a proportion near $48 \%$.

From a survey of coworkers, you find that $48 \%$ of 200 have already received this year's flu vaccine. An approximate $95 \%$ confidence interval is $(0.409,0.551)$, and you find that $48 \%$ of 200 have already received this year's flu vaccine. An approximate $95 \%$ confidence interval is $(0.409,0.551)$.

b) How would the confidence interval change if the confidence level had been $90 \%$ instead of $95 \%$ ?

From a survey of coworkers, you find that $48 \%$ of 200 have already received this year's flu vaccine. An approximate $95 \%$ confidence interval is $(0.409,0.551)$. Is the following true? If not, describe briefly.

c) There is a $95 \%$ chance that a randomly chosen coworker has received the vaccine.

From a survey of coworkers, you find that $48 \%$ of 200 have already received this year's flu vaccine. An approximate $95 \%$ confidence interval is $(0.409,0.551)$. Is the following true? If not, describe briefly.

b) We are $95 \%$ confident that the proportion of coworkers who have received this year's flu vaccine is between $40.9 \%$ and $55.1 \%$.

From a survey of coworkers, you find that $48 \%$ of 200 have already received this year's flu vaccine. An approximate $95 \%$ confidence interval is $(0.409,0.551)$. Is the following true? If not, describe briefly.

a) $95 \%$ of the coworkers fall in the interval $(0.409,0.551)$.

For the situation identify the population and the sample and identify $p$ and $\hat{p}$ if appropriate and what the value of $\hat{p}$ is. Would you trust a confidence interval for the true proportion based on these data? Describe briefly why or why not.

b) The website of the English newspaper The Guardian asked visitors to the site to say whether they approved of recent "bossnapping" actions by British workers who were outraged over being fired. Of those who responded, $49.2 \%$ said "Yes. Desperate times, desperate measures."

Just before a referendum on a school budget, a local newspaper polls 400 voters in an attempt to predict whether the budget will pass. Assume that the budget actually has the support of $52 \%$ of the voters. What's the chance the newspaper's sample will lead them to predict defeat? Be sure to verify that the assumptions and conditions necessary for your research are met.

Just before a referendum on a school budget, a local newspaper polls 400 voters in an attempt to predict whether the budget will pass. Suppose that the budget actually has the support of 52% of the voters. What’s the probability the newspaper’s sample will lead them to predict defeat? Be sure to verify that the assumptions and conditions necessary for your analysis are met.

For the situation identify the population and the sample and identify $p$ and $\hat{p}$ if appropriate and what the value of $\hat{p}$ is. Would you trust a confidence interval for the true proportion based on these data? Describe briefly why or why not.

a) As concertgoers enter a stadium, a security guard randomly inspects their backpacks for alcoholic beverages. Of the 130 backpacks checked so far, 17 contained alcoholic beverages of some kind. The guards want to estimate the percentage of all backpacks of concertgoers at this concert that contains alcoholic beverages.

A real estate agent wants to know how many owners of homes worth over $\$ 1,000,000$ might be thinking of putting their home on the market in the next 12 months. He surveys 40 of them and finds that 10 of them are considering such a move. Are all the assumptions and conditions for finding the sampling distribution of the proportion satisfied? Describe briefly.

An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via smartphones so they want to estimate the proportion of users who access the site that way (even if they also use their computers sometimes) . They draw a random sample of 200 investors from their customers. Suppose that the true proportion of smartphone users is 36%.

What would be the mean of this sampling distribution?

The proportion of adult women in the United States is about $51 \%$. A marketing survey telephones 400 people at random.

a) What is the sampling distribution of the observed proportion that is women?

Lately, two students made worldwide headlines by spinning a Belgian euro 250 times and getting 140 heads that's $56 \%$. That makes the $90 \%$ confidence interval $(51 \%, 61 \%)$. What does this imply? Are the conclusions in parts a-e correct? Describe your responses.

c) We are $90 \%$ sure that spun euros will land heads between $51 \%$ and $61 \%$ of the time.

A company packaging snack foods maintains quality control by randomly choosing 10 cases from each day's production and weighing the bags. Then they open one bag from each case and inspect the contents.

Identify the next items (if feasible). If you can't describe, then say so-this often happens when we read about a survey.

b) The population parameter of interest