According to the Gallup Poll, $27\%$ of U.S. adults have high levels of cholesterol. Gallup reports that such elevated levels "could be financially devastating to the U.S. healthcare system" and are a major concern to health insurance providers. According to recent analyses, cholesterol levels in healthy U.S. adults average about $215 \mathrm{mg} / \mathrm{dL}$ with a standard deviation of about $30 \mathrm{mg} / \mathrm{dL}$ and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy U.S. adults are taken,

d) If the sample size were increased to 100, how would your answers to parts a-c change?

The technology committee has stated that the average time spent by students per lab visit has increased, and the increase supports the need for increased lab fees. To substantiate this claim, the committee randomly samples 12 student lab visits and notes the amount of time spent using the computer. The times in minutes are as follows:

b) The last mean time spent using the lab computer was 55 minutes. Find a $95 \%$ confidence interval for the true mean. What do you conclude about the claim? If there are outliers, find intervals with and without the outliers present.

The technology committee has stated that the average time spent by students per lab visit has increased, and the increase supports the need for increased lab fees. To substantiate this claim, the committee randomly samples 12 student lab visits and notes the amount of time spent using the computer. The times in minutes are as follows:

Will your flight get you to your destination on time? The U.S. Bureau of Transportation Statistics reported the percentage of flights that were late each month from 1995 through early 2013. Here's a some summary statistics: Percent of Flights Delayed

We can consider these data to be a representative sample of all months. There is no evidence of a time trend.

c) Interpret this interval for a traveler planning to fly.

Will your flight get you to your destination on time? The U.S. Bureau of Transportation Statistics reported the percentage of flights that were late each month from 1995 through early 2013. Here's a some summary statistics: Percent of Flights Delayed

We can consider these data to be a representative sample of all months. There is no evidence of a time trend.

b) Find a $99 \%$ confidence interval for the true percentage of flights that arrive late.

What are the chances your flight will leave on time? The U.S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline performance. Here are summary statistics for the percentage of flights departing on time each month from 1995 through September 2011.

There is no evidence of a trend over time. (The correlation of On Time Departure% with time is $r=-0.016$.)

c) Interpret this interval for a traveler planning to fly.

What are the chances your flight will leave on time? The U.S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline performance. Here are summary statistics for the percentage of flights departing on time each month from 1995 through September 2011.

There is no evidence of a trend over time. (The correlation of On Time Departure% with time is $r=-0.016$.)

c) Interpret this interval for a traveler planning to fly.

What are the chances your flight will leave on time? The U.S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline performance. Here are summary statistics for the percentage of flights departing on time each month from 1995 through September 2011.

There is no evidence of a trend over time. (The correlation of On Time Departure% with time is $r=-0.016$.)

b) Find a $90 \%$ confidence interval for the mean percentage of flights that depart on time.

What are the chances your flight will leave on time? The U.S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline performance. Here are summary statistics for the percentage of flights departing on time each month from 1995 through September 2011.

There is no evidence of a trend over time. (The correlation of On Time Departure% with time is $r=-0.016$.)

a) Check the assumptions and conditions for inference.

States that depend on sales tax for revenue to fund education, public safety, and other programs often have budget surpluses during economic growth periods (when people spend more on consumer goods) and budget deficits during recessions (when people spend less on consumer goods). Fifty-one small retailers in a state with a growing economy were recently sampled. The sample showed a mean increase of $\$ 2350$ in additional sales tax revenue collected per retailer compared to the previous quarter. The sample standard deviation $=\$ 425$. Consider the state sampled 16 small retailers instead of 51. For the sample of 16, the sample mean increased again, equaling $\$ 2350$ in additional sales tax revenue collected per retailer compared to the previous quarter. Also, consider the sample standard deviation $=\$ 425$.

d) How does the margin of error for the interval constructed in Exercise 35 compare with the margin of error constructed in this exercise? Describe statistically how sample size changes the accuracy of the constructed interval. Which sample would you prefer if you were a state budget planner? Why?

States that depend on sales tax for revenue to fund education, public safety, and other programs often have budget surpluses during economic growth periods (when people spend more on consumer goods) and budget deficits during recessions (when people spend less on consumer goods). Fifty-one small retailers in a state with a growing economy were recently sampled. The sample showed a mean increase of $\$ 2350$ in additional sales tax revenue collected per retailer compared to the previous quarter. The sample standard deviation $=\$ 425$. Consider the state sampled 16 small retailers instead of 51. For the sample of 16, the sample mean increased again, equaling $\$ 2350$ in additional sales tax revenue collected per retailer compared to the previous quarter. Also, consider the sample standard deviation $=\$ 425$.

c) Find and analyze a $95 \%$ confidence interval.

States that depend on sales tax for revenue to fund education, public safety, and other programs often have budget surpluses during economic growth periods (when people spend more on consumer goods) and budget deficits during recessions (when people spend less on consumer goods). Fifty-one small retailers in a state with a growing economy were recently sampled. The sample showed a mean increase of $\$ 2350$ in additional sales tax revenue collected per retailer compared to the previous quarter. The sample standard deviation $=\$ 425$. Consider the state sampled 16 small retailers instead of 51. For the sample of 16, the sample mean increased again, equaling $\$ 2350$ in additional sales tax revenue collected per retailer compared to the previous quarter. Also, consider the sample standard deviation $=\$ 425$.

b) What happens to the estimate's accuracy when the interval is constructed using a smaller sample size?

States that depend on sales tax for revenue to fund education, public safety, and other programs often have budget surpluses during economic growth periods (when people spend more on consumer goods) and budget deficits during recessions (when people spend less on consumer goods). Fifty-one small retailers in a state with a growing economy were recently sampled. The sample showed a mean increase of $\$ 2350$ in additional sales tax revenue collected per retailer compared to the previous quarter. The sample standard deviation $=\$ 425$. Consider the state sampled 16 small retailers instead of 51. For the sample of 16, the sample mean increased again, equaling $\$ 2350$ in additional sales tax revenue collected per retailer compared to the previous quarter. Also, consider the sample standard deviation $=\$ 425$.

a) What is the standard error of the mean increase in sales tax revenue collected?

States that depend on sales tax for revenue to fund education, public safety, and other programs often end up with budget surpluses during economic growth periods (when people spend more on consumer goods) and budget deficits during recessions (when people spend less on consumer goods). Fifty-one small retailers in a state with a growing economy were recently sampled. The sample showed a mean increase of $\$ 2350$ in additional sales tax revenue collected per retailer compared to the previous quarter. The sample standard deviation $=\$ 425$.

c) Describe what your interval means and provide an example of what it does not mean.