91影视

Suppose that $14$children, who were learning to ride two-wheel bikes, were surveyed to determine how long they had

to use training wheels. It was revealed that they used them an average of six months with a sample standard deviation of

three months. Assume that the underlying population distribution is normal.

$$\begin{gathered} a.i.x虅=\_\_\_\_\_\_\_\_\_\_ \\ ii.s_x=\_\_\_\_\_\_\_\_\_\_ \\ iii.n=\_\_\_\_\_\_\_\_\_\_ \\ iv.n鈥�1=\_\_\_\_\_\_\_\_\_\_ \end{gathered}$$

b. Define the random variable $X$in words.

c. Define the random variable $\overline{X}$in words.

d. Which distribution should you use for this problem? Explain your choice.

e. Construct a $99\%$confidence interval for the population mean length of time using training wheels.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

f. Why would the error bound change if the confidence level were lowered to $90\%$?

The Federal Election Commission (FEC) collects information about campaign contributions and disbursements for

candidates and political committees each election cycle. A political action committee (PAC) is a committee formed to raise

money for candidates and campaigns. A Leadership PAC is a PAC formed by a federal politician (senator or representative)

to raise money to help other candidates鈥� campaigns.

The FEC has reported financial information for $556$Leadership PACs that operating during the $2011鈥�2012$election cycle.

The following table shows the total receipts during this cycle for a random selection of $30$Leadership PACs.

虅$\overline{x}$$=\backslash (251,854.23$

$s=\backslash )521,130.41$

Use this sample data to construct a $96\%$confidence interval for the mean amount of money raised by all Leadership PACs

during the $2011鈥�2012$election cycle. Use the Student's t-distribution.

If the Census did another survey, kept the error bound the same, and surveyed only $50$ people instead of $200$, what would happen to the level of confidence? Why?

Forbes magazine published data on the best small firms in $2012$. These were firms that had been publicly traded for at least a year, have a stock price of at least $\backslash (5$per share, and have reported annual revenue between $\backslash )5$million and$\$1$ billion.

The Table 8.13 shows the ages of the corporate CEOs for a random sample of these firms.

Use this sample data to construct a $90\%$confidence interval for the mean age of CEO鈥檚 for these top small firms. Use the Student's t-distribution.

Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its mean number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.6 seats and the sample standard deviation is 4.1 seats.

a. i. $\overline{x}=$__________

ii. $s_x=$__________

iii. $n=$__________

iv. $n-1=$__________

b. Define the random variables $X$and $\overline{X}$in words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 92% confidence interval for the population mean number of unoccupied seats per flight.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

In a recent sample of $84$used car sales costs, the sample mean was $\backslash (6,425$with a standard deviation of $\backslash )3,156$. Assume

the underlying distribution is approximately normal.

a. Which distribution should you use for this problem? Explain your choice.

b. Define the random variable$\overline{X}$in words.

c. Construct a $95\%$confidence interval for the population mean cost of a used car.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

d. Explain what a 鈥�$95\%$ confidence interval鈥� means for this study.

Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The grams of fat per serving are as follows: $8;8;10;7;9;9$. Assume the underlying distribution is approximately normal.

a. Construct a $90\%$confidence interval for the population mean grams of fat per serving of chocolate chip cookies

sold in supermarkets.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

b. If you wanted a smaller error bound while keeping the same level of confidence, what should have been changed in the study before it was done?

c. Go to the store and record the grams of fat per serving of six brands of chocolate chip cookies.

d. Calculate the mean.

e. Is the mean within the interval you calculated in part a? Did you expect it to be? Why or why not?

A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20垄; 75垄; 50垄; 65垄; 30垄; 55垄; 40垄; 40垄; 30垄; 55垄; $1.50; 40垄; 65垄; 40垄. Assume the underlying distribution is approximately normal.

a. i. $\stackrel{-}{x}$= __________

ii. $s_x$= __________

iii. n = __________

iv. n-1 = __________

b. Define the random variables $X$and$\stackrel{-}{X}$ in words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 95% confidence interval for the population mean worth of coupons.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. If many random samples were taken of size 14, what percent of the confidence intervals constructed should contain the population mean worth of coupons? Explain why.

Use the following information to answer the next two exercises: A quality control specialist for a restaurant chain takes a random sample of size 12 to check the amount of soda served in the 16 oz. serving size. The sample mean is 13.30 with a sample standard deviation of 1.55. Assume the underlying population is normally distributed.

115. Find the 95% Confidence Interval for the true population mean for the amount of soda served.

a. (12.42, 14.18)

b. (12.32, 14.29)

c. (12.50, 14.10)

d. Impossible to determine

Insurance companies are interested in knowing the population per cent of drivers who always buckle up before riding in a car.

a. When designing a study to determine this population proportion, what is the minimum number you would need to survey to be 95% confident that the population proportion is estimated to be within 0.03?

b. If it were later determined that it was important to be more than 95% confident and a new survey was commissioned, how would that affect the minimum number you would need to survey? Why?