In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. The professor then makes a histogram of the reported proportions.

b) Confirm that you can use a Normal model here.

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. The professor then makes a histogram of the reported proportions.

c) How much variability would you anticipate among these proportions?

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. The professor then makes a histogram of the reported proportions.

a) The students use computer-generated random numbers to choose 25 stocks each. Use the 68-95-99.7 Rule to describe the sampling distribution model.

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. The professor then makes a histogram of the reported proportions.

c) They increase the number of stocks picked to 64 each. Draw and label the appropriate sampling distribution model. Check the appropriate conditions to justify your model.

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. He watches a cable news show about investing and during the show throws his darts at the pages of the Journal. He claims that of 200 stocks picked in this manner, $58 \%$ were winners.

b) If there are 100 students in the class, are you surprised that one was this successful? Explain.

Identify the sample and the population for each situation. Then describe the sample statistic and the population parameter. A random sample of 1000 U.S. college students is surveyed about how much they spend on books per year.

Identify the sample and the population of the situation. Then describe the sample statistic and the population parameter. A random sample of 1003 Mercy County voters is asked if they would vote for the incumbent for governor. The percent responding yes is calculated.

Identify the sample and the population for the situation. Then describe the sample statistic and the population parameter.

A veterinarian randomly selects 3 kittens from a litter. The mean weight of the 3 kittens is calculated.

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 $(0.409,0.551)$.

a) How would the confidence interval change if the sample size had been 800 instead of 200?

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.

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

c) How would the confidence interval change if the confidence level had been $99 \%$ 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.

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

Explain why the critical value for a given confidence level when the population variance is not known is always greater than the critical value for the same confidence level when the population variance is known.

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 $95 \%$ ?