An engineer selects 10 components at random and measures their strengths. It is reported that the average strength of the components is between 72.3 and 74.5 with 99$\%$ confidence. (a) What is the sample standard deviation of the 10 component strengths? (b) If a 99$\%$ two-sided confidence interval is desired with a length no longer than 1.0, about how many additional components would you recommend be tested?

A sample of 14 fibers was tested. Their strengths had a sample average of 266.5 and a sample standard deviation of 18.6. Use a hypothesis test to assess whether it is safe to conclude that the average strength of fibers of this type is at least 260.0.

Integrate the given function over the given surface.

$$G ( x , y , z ) = x ^ { 2 },$$

over the unit sphere

$$x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1.$$

Write a paragraph explaining how the scientific method exemplified the new emphasis on reason.

Write your own definition for each content and academic vocabulary term. Content Vocabulary: marketing, goods, services, marketing concept, utility, market, consumer market, organizational market, market share, target market, customer profile, marketing mix. Academic Vocabulary: create, conduct, impact, benefits, similar, elements.

Which equation does not represent a line with an x-intercept of 3?

(A) $y=-2x+6$

(B) $y=-\dfrac{1}{3}x+1$

(C) $y=\dfrac{2}{3}x-2$

(D) $y=3x-1$

What are the eight main types of daily hassles?

Factor the matrix

$$A=\left[\begin{array}{rrrr}{0} & {1} & {7} & {8} \\ {1} & {3} & {3} & {8} \\ {-2} & {-5} & {1} & {-8}\end{array}\right]$$

as A=EFGR, where E, F, and G are elementary matrices and R is in row echelon form.

Primo Management Co. is looking at how best to evaluate the performance of its managers. Primo has been hearing more and more about benchmark portfolios and is interested in trying this approach. As such, the company hired Sally Jones, CFA, as a consultant to educate the managers on the best methods for constructing a benchmark portfolio, how best to choose a benchmark, whether the style of the fund under management matters, and what they should do with their global funds in terms of benchmarking. For the sake of discussion, Jones put together some comparative two-year performance numbers that relate to Primo’s current domestic funds under management and a potential benchmark. $$ \begin{matrix} \text{Style Category} & \text{Weight Primo} & \text{Weight Benchmark} & \text{Return Primo} & \text{Return Benchmark}\\ \text{Large-cap growth} & \text{0.60} & \text{0.50} & \text{17\\%} & \text{16\\%}\\ \text{Mid-cap growth} & \text{0.15} & \text{0.40} & \text{24} & \text{26}\\ \text{Small-cap growth} & \text{0.25} & \text{0.10} & \text{20} & \text{18}\\ \end{matrix} $$ As part of her analysis, Jones also takes a look at one of Primo’s global funds. In this particular portfolio, Primo is invested 75% in Dutch stocks and 25% in British stocks. The benchmark invested 50% in each—Dutch and British stocks. On average, the British stocks outperformed the Dutch stocks. The euro appreciated 6% versus the U.S. dollar over the holding period, while the pound depreciated 2% versus the dollar. In terms of the local return, Primo outperformed the benchmark with the Dutch investments but underperformed the index with respect to the British stocks. If Primo decides to use return-based style analysis, will the R2 of the regression equation of a passively managed fund be higher or lower than that of an actively managed fund?

A sample of $n = 18$ observations has a sample standard deviation of $s = 6.48$. Construct $99\%$ and $95\%$ two-sided confidence intervals for the population variance $\sigma^2$.

If your computer reports a $p$-value of 0.005, then: A. The probability that the alternative hypothesis is true is 0.005. B. The data has almost certainly been faked. C. The chance of getting the data set or worse when the null hypothesis is true is 1 out of 200. D. The computer software package has certainly made a mistake.

Customers at Big Burger spend an average of $6.15 with a standard deviation of$0.75. (a) Estimate the percentage of customers who spend more than $7.00.

An experimenter is interested in the hypothesis testing problem

$$H_0 : \mu \ge 420.0 \text{ versus } H_A : \mu < 420.0$$

where $\mu$ is the average radiation level in a research laboratory. Suppose that a sample of $n = 29$ radiation level measurements is obtained and that the experimenter wishes to use a value of $\sigma = 10.0$ for the standard deviation of the radiation levels. (a) For what values of the $z$-statistic does the experimenter $\textit{accept}$ the null hypothesis with a size $\alpha =0.10$? (b) For what values of the $z$-statistic does the experimenter $\textit{reject}$ the null hypothesis with a size $\alpha = 0.01$? Suppose that the sample mean is $\bar{x} = 415.7$. (a) Is the null hypothesis accepted or rejected with $\alpha = 0.10$? With $\alpha = 0.01$? (b) Calculate the exact $p$-value.

An experimenter randomly selects $n = 16$ batteries from a production line and measures their voltages. An average $\bar{x} = 239.13$ is obtained, with a sample standard deviation $s = 2.80$. Does this experiment provide sufficient evidence for the experimenter to conclude that the average voltage of the batteries from the production line is at least 238.5?