A Marketing Firm Asked a Random Set of Married and Single

question 42

Multiple Choice

A marketing firm asked a random set of married and single men how much they were willing to spend on a vacation. Is there sufficient evidence at $\alpha = 0.05$ to conclude that is there a difference in the two amounts?
$\begin{array}{lcc}\hline & \text { Married Men } & \text { Single Men } \\\hline \text { Sample size } & 70 & 70 \\\text { Sample mean } & \$ 880 & \$ 825 \\\text { Population variance } & 5700 & 7900 \\\hline\end{array}$

• A) Yes, because the test value \(3.95\) is outside the critical region \(- 1.96 < z < 1.96\).
• B) Yes, because the test value \(1.39\) is inside the critical region \(- 1.96 < z < 1.96\).
• C) No, because the test value \(0.28\) is inside the critical region \(- 1.96 < z < 1.96\).
• D) No, because the test value \(1.39\) is outside the critical region \(- 1.96 < z < 1.96\).

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Definitions:

Optimal Risky Portfolio

An investment portfolio that offers the highest expected return for a given level of risk or the lowest risk for a given level of expected return.

Beta

A measure of a security's volatility in relation to the overall market, indicating the security's risk compared to the market average.

Sensitive

Quick to detect or respond to slight changes, signals, or influences.

Standard Deviation

A statistic that measures the dispersion or variability of a dataset relative to its mean, often used in finance to represent the volatility of an investment.