Although founded only in $2004$, Facebook has more than $500$ million active users, of which 50% log on to Facebook on any given day. In a recent survey by Facebook, young users (those born after 1984) were asked about their preference for delivering the news about breaking up a relationship (The Wall Street Journal, November 27-28, 2010). One of the shocking results was that only 47% of users preferred to break the news in person. A researcher decides to verify the survey results of Facebook by taking her own sample of $200$ young Facebook users. The preference percentages from Facebook and the researcher's survey are presented in the following table.

$$\begin{array}{|l|c|c|} \hline \begin{array}{l} \text { Delivery } \\ \text { Method } \end{array} & \begin{array}{c} \text { Facebook } \\ \text { Results } \end{array} & \begin{array}{c} \text { Researcher's } \\ \text { Results } \end{array} \\ \hline \text { In Person } & 47 \% & 55 \% \\ \hline \text { Phone } & 30 \% & 28 \% \\ \hline \text { Email } & 4 \% & 8 \% \\ \hline \text { Facebook } & 5 \% & 3 \% \\ \hline \text { Instant Message } & 14 \% & 6 \% \\ \hline \end{array}$$

At the 5% level of significance, test if the researcher's results are inconsistent with the survey results conducted by Facebook. Provide the details, using the $p$-value approach.

A study suggests that airlines have increased restrictions on cheap fares by raising overnight requirements (The Wall Street Journal, August 19, 2008). This would force business travelers to pay more for their flights, since they tend to need the most flexibility and want to be home on weekends Eight months ago, the overnight stay requirements were as follows:

$$\begin{array}{|c|c|c|c|} \hline \text { One night } & \text { Two nights } & \begin{array}{c} \text { Three } \\ \text { nights } \end{array} & \begin{array}{c} \text { Saturday } \\ \text { night } \end{array} \\ \hline 37 \% & 17 \% & 28 \% & 18 \% \\ \hline \end{array}$$

A recent sample of $644$ flights found the following restrictions:

$$\begin{array}{|c|c|c|c|} \hline \text { One night } & \text { Two nights } & \begin{array}{c} \text { Three } \\ \text { nights } \end{array} & \begin{array}{c} \text { Saturday } \\ \text { night } \end{array} \\ \hline 117 & 137 & 298 & 92 \\ \hline \end{array}$$

a. Specify the competing hypotheses to test whether the proportions cited by the study have changed.

b. At a 5% significance level, what is the critical value?

c. Calculate the value of the test statistic.

d. What is the conclusion to the hypothesis test? Interpret your results.

The following table lists the market shares of the four firms in a particular industry in 2010 and total sales for each firm in $2011 .$

$$\begin{array}{|c|c|c|} \hline \text { Firm } & \begin{array}{c} \text { Market Share } \\ \text { in } 2010 \end{array} & \begin{array}{c} \text { Total Sales in } \\ 2011 \text { (in billions } \\ \text { of } \$ \text { ) } \end{array} \\ \hline 1 & 0.40 & 200 \\ \hline 2 & 0.30 & 180 \\ \hline 3 & 0.20 & 100 \\ \hline 4 & 0.10 & 70 \\ \hline \end{array}$$

a. Specify the competing hypotheses to test whether the market shares in $2010$ are not valid in $2011.$

b. At the 1% significance level, what is the critical value?

c. Calculate the value of the test statistic.

d. Do the sample data suggest that the market shares changed from $2010$ to $2011 ?$

The data that accompanies this exercise show miles per gallon (MPG) for a sample of 25 cars.

a. Using the Jarque-Bera test, state the competing hypotheses in order to determine whether or not MPG follow the normal distribution.

b. Calculate the value of the Jarque-Bera test statistic. Use Excel to calculate the $p$-value.

c. At $\alpha=0.05$, can you conclude that MPG are not normally distributed?

The data that accompanies this exercise show weekly stock prices for Home Depot.

a. Using the Jarque-Bera test, state the competing hypotheses in order to determine whether or not Home Depot's weekly stock prices follow the normal distribution.

b. Calculate the value of the Jarque-Bera test statistic. Use Excel to calculate the $p$-value.

c. At $\alpha=0.05$, can you conclude that Home Depot's stock prices are not normally distributed?

Rank the following nonmetals from lowest number of electrons in the outer level to highest: $Cl^-, H^+, He, H.$

The following frequency distribution shows the distribution of monthly returns for Starbucks Corp. for the years 2003 through $2007.$

$$\begin{array}{|l|c|} \hline \text { Class (in percent) } & \text { Frequency } \\ \hline \text { Less than }-5 & 14 \\ \hline-5 \text { up to } 0 & 9 \\ \hline 0 \text { up to } 5 & 18 \\ \hline 5 \text { up to } 10 & 11 \\ \hline 10 \text { or more } & 8 \\ \hline & n=60 \\ \hline \end{array}$$

Over this time period, the following summary statistics are provided:

$$\begin{array}{|c|c|c|c|c|} \hline \text { Mean } & \text { Median } & \begin{array}{c} \text { Standard } \\ \text { Deviation } \end{array} & \text { Skewness } & \text { Kurtosis } \\ \hline 1.16 \% & 1.79 \% & 7.38 \% & -0.31 & -0.65 \\ \hline \end{array}$$

a. Conduct a goodness-of-fit test for normality at the 5% significance level. Can you conclude that monthly returns do not follow the normal distribution?

b. Conduct the Jarque-Bera test at the 5% significance level. Can you conclude that monthly returns do not follow the normal distribution?

The mass of an alpha particle is 4.0026 mass units, and the mass of a beta particle is 0.000548 mass units. How many times larger is the mass of an alpha particle than the mass of a beta particle?

Total 2005 CE0 compensation for the largest U.S. companies by revenue is reported in the following frequency distribution, along with some summary statistics. Total compensation includes salary, bonuses, stock and incentives, the potential value of stock options, and gains from stock options exercised.

$$\begin{array}{|l|c|} \hline \begin{array}{l} \text { Total Compensation } \\ \text { (in millions of \$) } \end{array} & \text { Frequency } \\ \hline \text { Less than } 5 & 43 \\ \hline 5 \text { up to } 10 & 65 \\ \hline 10 \text { up to } 15 & 32 \\ \hline 15 \text { up to } 20 & 38 \\ \hline 20 \text { or more } & 60 \\ \hline & n=238 \\ \hline \end{array}$$

Other summary statistics for CEO compensation (in millions of $) are as follows:$

$$\begin{array}{|c|c|c|c|c|} \hline \text { Mean } & \text { Median } & \begin{array}{c} \text { Standard } \\ \text { Deviation } \end{array} & \text { Skewness } & \text { Kurtosis } \\ \hline 19.03 & 11.02 & 27.61 & 5.26 & 35.53 \\ \hline \end{array}$$

$a. Conduct a goodness-of-fit test for normality of CEO compensation at the 1% significance level.

b. Conduct the Jarque-Bera test at the 1$ significance level.

c. Does total compensation of CEOs for the largest U.S. companies not follow the normal distribution?

Fabco, a precision machining shop, uses statistical process control (SPC) techniques to ensure quality and consistency of their steel shafts. The control limits used in their SPC charts are based on the assumption that shaft diameters are normally distributed. To verify this assumption, a quality engineer has measurec the diameters for a sample of 50 of its popular 1/2-inch shafts.

a. Using the Jarque-Bera test, state the competing hypotheses in order to determine whether or not the data follow the normal distribution.

b. Calculate the value of the Jarque-Bera test statistic Use Excel to calculate the $p$-value.

c. At $\alpha=0.10$, can you conclude that the shaft diameters are not normally distributed?

d. Would your conclusion change at the 5% significance level?

The quality department at an electronics component manufacturer must ensure that their components will operate at prespecified levels. The accompanying table shows a frequency distribution with measured resistance values (in ohms) for a sample of $520$ resistors. The sample mean and the sample standard deviation are $4790 \mathrm{ohms}$ and 40 ohms, respectively.

$$\begin{array}{|l|c|} \hline \text { Resistance (ohms) } & \text { Frequency } \\ \hline \text { Under } 4740 & 44 \\ \hline 4740 \text { up to } 4780 & 145 \\ \hline 4780 \text { up to } 4820 & 197 \\ \hline 4820 \text { up to } 4860 & 107 \\ \hline 4860 \text { or more } & 27 \\ \hline & \text { Total }=520 \\ \hline \end{array}$$

a. Using the goodness-of-fit test for normality, state the competing hypotheses to test if the sample data suggest that resistance does not follow the normal distribution.

b. At $\alpha=0.05$, what is the critical value?

c. Calculate the value of the test statistic.

d. What is the conclusion to the test? Would your conclusion change at the 10% significance level?

Why did scientists choose carbon to base the atomic mass unit? Which isotope of carbon did they use?

SOCIAL SCIENCE: Population The population of the world x years after the year 2010 is predicted to be $6.9 e^{0.00743 x}$ billion people (for $0 \leq x \leq 30$ ). Use this formula to predict the world population in the year 2030 .

Chlorine has an average atomic mass of 35.45 amu. The two naturally occurring isotopes of chlorine are chlorine-35 and chlorine-37. Why does this indicate that most chlorine atoms contain 18 neutrons?