The Employment and Training Administration reported that the U.S. mean unemployment insurance benefit was $238 per week (The World Almanac, 2003). A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was below the national average.

Develop appropriate hypotheses such that rejection of H0 will support the researcher’s contention.

In a study entitled How Undergraduate Students Use Credit Cards, it was reported that undergraduate students have a mean credit card balance of $3173 (Sallie Mae, April 2009). This figure was an all-time high and had increased 44that a current study is being conducted to determine if it can be concluded that the mean credit card balance for undergraduate students has continued to increase compared to the April 2009 report. Based on previous studies, use a population standard deviation$\sigma$=$1000.

a. State the null and alternative hypotheses.

b. What is the p-value for a sample of 180 undergraduate students with a sample mean credit card balance of $3325?

c. Using a .05 level of significance, what is your conclusion?

The rate of reaction r to a given dose of a drug at time t hours after administration is given by $r(t)=t e^{-t^{2}}$ (measured in appropriate units). (a) Why is it reasonable to define the total reaction as the area under the graph of y=r(t) on $[0, \infty)$? (b) Find the total reaction to the given dose of the drug.

A learning management system is part of which of the following HRIS components?

a) Employment equity;

b) Performance evaluation;

c) Organizational management;

d) Training and development;

e) Employee administration

Consider the following hypothesis test:

$$\begin{array} { l } { H _ { 0 } : \mu \leq 12 } \\ { H _ { \mathrm { a } } : \mu > 12 } \end{array}$$

A sample of 25 provided a sample mean $\overline { x } = 14$ and a sample standard deviation $s = 4.32$.

Compute the value of the test statistic.

Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 15 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. A sample of 35 surveys provided the survey times shown in the file named Fowle. Based upon past studies, the population standard deviation is assumed known with $\sigma$ = 4 minutes. Is the premium rate justified?

Formulate the null and alternative hypotheses for this application.

Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed within 15 minutes or less. If more time is required, a premium rate is charged. With a sample of 35 surveys, a population standard deviation of 4 minutes, and a level of significance of .01, the sample mean will be used to test the null hypothesis

$$H _ { 0 } : \mu \leq 15$$

a. What is your interpretation of the Type II error for this problem? What is its impact on the firm? b. What is the probability of making a Type II error when the actual mean time is $\mu$= 17 minutes? c. What is the probability of making a Type II error when the actual mean time is $\mu$= 18 minutes? d. Sketch the general shape of the power curve for this test.

For the United States, the mean monthly Internet bill is $32.79 per household (CNBC, January 18, 2006). A sample of 50 households in a southern state showed a sample mean of$30.63. Use a population standard deviation of $\sigma$= $5.60.

Formulate hypotheses for a test to determine whether the sample data support the conclusion that the mean monthly Internet bill in the southern state is less than the national mean of$32.79.

Speaking to a group of analysts in January 2006, a brokerage firm executive claimed that at least 70% of investors are currently confident of meeting their investment objectives. A UBS Investor Optimism Survey, conducted over the period January 2 to January 15, found that 67% of investors were confident of meeting their investment objectives (CNBC, January 20, 2006).

Formulate the hypotheses that can be used to test the validity of the brokerage firm executive’s claim.

Consider the following hypothesis test:

$$\begin{array} { l } { H _ { 0 } : \mu \geq 45 } \\ { H _ { \mathrm { a } } : \mu < 45 } \end{array}$$

A sample of 36 is used. Identify the $p$ -value and state your conclusion for each of the fol- lowing sample results. Use $\alpha = .01 .$

$\overline { x } = 44$ and $s = 5.2$

Individuals filing federal income tax returns prior to March 31 received an average refund of $\$1056$. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15).

a. A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of $\ H_0$ will support the researcher’s contention.

b. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $\$910$. Based on prior experience a population standard deviation of $\sigma$ =$\$1600$ may be assumed. What is the p-value?

c. At $\alpha$ = .05, what is your conclusion?

d. Repeat the preceding hypothesis test using the critical value approach.

Individuals filing federal income tax returns prior to March 31 received an average refund of $1056. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15).

A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcher’s contention.

CCN and ActMedia provided a television channel targeted to individuals waiting in supermarket checkout lines. The channel showed news, short features, and advertisements. The length of the program was based on the assumption that the population mean time a shopper stands in a supermarket checkout line is 8 minutes. A sample of actual waiting times will be used to test this assumption and determine whether actual mean waiting time differs from this standard.

Formulate the hypotheses for this application.

Individuals filing federal income tax returns prior to March 31 received an average refund of $1056. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15).

At$\alpha = .05$, what is your conclusion?