Related questions with answers

Advertising researchers have developed a theory that states that commercials that appear in violent television shows are less likely to be remembered and will thus be less effective. After examining samples of viewers who watch violent and nonviolent programs and asking them a series of five questions about the commercials, the researchers produced the following probability distributions of the number of correct answers. Calculate the mean and standard deviation of the number of correct answers among viewers of violent television programs.

Viewers of violent shows:

$\boldsymbol{x}$	0	1	2	3	4	5
$\boldsymbol{P}(\boldsymbol{x})$	$.36$	$.22$	$.20$	$.09$	$.08$	$.05$

Viewers of nonviolent shows:

$\boldsymbol{x}$	0	1	2	3	4	5
$\boldsymbol{P}(\boldsymbol{x})$	$.15$	$.18$	$.23$	$.26$	$.10$	$.08$

Below are departmental income statements for a guitar manufacturer. The manufacturer is considering eliminating its electric guitar department since it has a net loss. The company classifies advertising, rent, and utilities expenses as indirect.

\begin{matrix} \text{WHOLESALE GUITARS Departmental Income Statements For Year Ended December 31, 2017}\\ & \text{Acoustic} & \text{Electric}\\ \text{Sales}\ldots\ldots\ldots & \text{\$112,500} & \text{\$105,500}\\ \text{Cost of goods sold}\ldots\ldots\ldots & \text{55,675} & \text{66,750}\\ \text{Gross profit} \ldots\ldots\ldots & \text{56,825} & \text{38,750}\\ \text{Operating expenses}\\ \text{Advertising expense}\ldots\ldots\ldots & \text{8,075} & \text{6,250}\\ \text{Depreciation expense—Equipment}\ldots\ldots\ldots & \text{10,150} & \text{9,000}\\ \text{Salaries expense}\ldots\ldots\ldots & \text{17,300} & \text{13,500}\\ \text{Supplies expense}\ldots\ldots\ldots & \text{2,030} & \text{1,700}\\ \text{Rent expense }\ldots\ldots\ldots & \text{6,105} & \text{5,950}\\ \text{Utilities expense}\ldots\ldots\ldots & \text{3,045} & \text{2,550}\\ \text{Total operating expenses}\ldots\ldots\ldots & \text{46,705} & \text{38,950}\\ \text{Net income (loss)}\ldots\ldots\ldots & \text{\$ 10,120} & \text{\$ (200)}\\ \end{matrix}

Prepare a departmental contribution report that shows each department’s contribution to overhead. 2. Based on contribution to overhead, should the electric guitar department be eliminated?

In an article in the Journal of Advertising, Weinberger and Spotts compare the use of humor in television ads in the United States and in the United Kingdom. Suppose that independent random samples of television ads are taken in the two countries. A random sample of $400$ television ads in the United Kingdom reveals that $142$ use humor, while a random sample of $500$ television ads in the United States reveals that $122$ use humor.

Calculate a $95$ percent confidence interval for the difference between the proportion of U.K. ads using humor and the proportion of U.S. ads using humor. Interpret this interval. Can we be $95$ percent confident that the proportion of U.K. ads using humor is greater than the proportion of U.S. ads using humor?