For the given situation, state whether a Type I, a Type II, or neither error has been made. Describe briefly.

c) A human resource analyst wants to know if the applicants this year score, on average, higher on their placement exam than the $52.5$ points the candidates averaged last year. She samples 50 recent tests and finds the average to be $54.1$ points. She fails to reject the null hypothesis that the mean is $52.5$ points. At the end of the year, they find that the candidates this year had a mean of $55.3$ points.

Two strips of brass, each $3.00 \mathrm{~cm}$ wide and $45.0 \mathrm{~cm}$ long, are placed with their ends overlapping by $1.00 \mathrm{~cm}$. The overlapping ends are then riveted together by four rivets, each with diameter $0.250 \mathrm{~cm}$. Tests show that when a tension of at least $1.20 \times 10^{-4} \mathrm{~N}$ is applied to the ends of the riveted strip, the rivets fail and shear apart. What shearing stress is applied to each rivet prior to failure? Assume that a fourth of the load is carried by each rivet.

The president of a large company with $10,000$ employees is considering mandatory cocaine testing for every employee. The test that would be used is $90\%$ accurate, meaning that it will detect $90\%$ of the cocaine users who are tested, and that $90\%$ of the nonusers will test negative. This also means that the test gives $10\%$ false positive. Suppose that $1\%$ of the employees actually use cocaine. Find the probability that someone who tests positive for cocaine use is indeed a user.

Hint: Find the following probability fraction:

$$\dfrac{\text{the number of employees who test positive and are cocaine users}}{\text{the number of employees who test positive}}$$

This fraction is given by

$$\dfrac{\text{90\% or 1\% of 10,000}}{\text{the number who test positive who actually use cocaine plus the number who test positive who do not use cocaine}}$$

What does this probability indicate in terms of the percentage of employees who test positive who are not actually users? Discuss these numbers in terms of the issue of mandatory drug testing. Write a paper either in favor of or against mandatory drug testing incorporating the actual percentage accuracy for such tests.

Read the passage below. Then answer the question.

Genetic counselors use various types of information, including pedigrees, laboratory tests, and karyotypes, to determine the odds of a person or a couple's child having a genetic disorder. Genetic counselors also outline the options for dealing with those risks and offer emotional support.

A man and a woman who do not have hemophilia visit a genetic counselor. What tool might the counselor use to determine the risk of the couple having a child with hemophilia?

A. blood test

B. DNA fingerprint

C. karyotype

D. pedigree

G.R. is a successful collage artist. He works with adhesives, paints, and solvents, which often must be heated to produce textured artworks. During the summer months he works out of doors and in the colder weather works in his studio, which is equipped with an exhaust fan. On very cold days he sometimes turns off the fan. He has been working very long hours to prepare for his upcoming winter show. Several times in the past few days he has commented to his partner that he feels weak, nauseated, and unable to work. He has noticed that he is not producing as much urine and thinks that this is due to decreased fluid intake during work. His partner contacts his doctor and takes him to the emergency department as directed. When seen in the emergency clinic, his blood pressure is 170/96, he has an abnormal pulse, and blood tests reveal elevated BUN, $K^{+}$, and creatinine levels. Further tests lead to a diagnosis of acute renal failure due to tubular necrosis. What are possible causes of acute renal failure in this case?

An automobile is to travel through standard air at $60\ \mathrm{mph}$. To determine the pressure distribution, a $\frac{1}{5}$-scale model is to be tested in water. What factors must be considered to ensure kinematic similarity in the tests? Determine the water speed that should be used. What is the corresponding ratio of drag force between prototype and model flows? The lowest pressure coefficient is $C_p=-1.4$ at the location of the minimum static pressure on the surface. Estimate the minimum tunnel pressure required to avoid cavitation, if the onset of cavitation occurs at a cavitation number of $0.5$.

Make the following hypothesis tests. a. $H_0: \mu=25, \quad H_1: \mu \neq 25, \quad n=81, \quad \bar{x}=28.5, \quad \sigma=3, \quad \alpha=.01$ b. $H_0: \mu=12, \quad H_1: \mu<12, \quad n=45, \quad \bar{x}=11.25, \quad \sigma=4.5, \quad \alpha=.05$ c. $H_0: \mu=40, \quad H_1: \mu>40, \quad n=100, \quad \bar{x}=47, \quad \sigma=7, \quad \alpha=.10$

PCR has been used to examine oysters for the presence of Vibrio cholerae. Oysters from different areas were homogenized, and DNA was extracted from the homogenates. TheDNA was digested by the restriction enzyme HincII. A primer for the hemolysin gene of V. cholerae was used for the PCR reaction. After PCR, each sample was electrophoresed and stained with a probe for the hemolysin gene. Which of the oyster samples were (was) positive for V. cholerae? How can you tell? Why look for V. cholerae in oysters? What is the advantage of PCR over conventional biochemical tests to identify the bacteria?

G.R. is a successful collage artist. He works with adhesives, paints, and solvents, which often must be heated to produce textured artworks. During the summer months he works out of doors and in the colder weather works in his studio, which is equipped with an exhaust fan. On very cold days he sometimes turns off the fan. He has been working very long hours to prepare for his upcoming winter show. Several times in the past few days he has commented to his partner that he feels weak, nauseated, and unable to work. He has noticed that he is not producing as much urine and thinks that this is due to decreased fluid intake during work. His partner contacts his doctor and takes him to the emergency department as directed. When seen in the emergency clinic, his blood pressure is 170/96, he has an abnormal pulse, and blood tests reveal elevated BUN, $K^{+}$, and creatinine levels. Further tests lead to a diagnosis of acute renal failure due to tubular necrosis. How have the kidneys been damaged; will they recover normal function?

G.R. is a successful collage artist. He works with adhesives, paints, and solvents, which often must be heated to produce textured artworks. During the summer months he works out of doors and in the colder weather works in his studio, which is equipped with an exhaust fan. On very cold days he sometimes turns off the fan. He has been working very long hours to prepare for his upcoming winter show. Several times in the past few days he has commented to his partner that he feels weak, nauseated, and unable to work. He has noticed that he is not producing as much urine and thinks that this is due to decreased fluid intake during work. His partner contacts his doctor and takes him to the emergency department as directed. When seen in the emergency clinic, his blood pressure is 170/96, he has an abnormal pulse, and blood tests reveal elevated BUN, $K^{+}$, and creatinine levels. Further tests lead to a diagnosis of acute renal failure due to tubular necrosis. Explain how hypertension has developed in G.R.

In exercise,

(a) write the claim mathematically and identify $H_0$ and $H_a$,

(b) find the critical value(s) and identify the rejection region(s),

(c) use the $X^2$-t est to find the standardized test statistic,

(d) decide whether to reject or fail to reject the null hypothesis, and

(e) interpret the decision in the context of the original claim. For each claim, assume the population is normally distributed.

On a physical science assessment test , the scores of a random sample of 22 eighth grade students have a standard deviation of 27.7. This result prompts a test administrator to claim that the standard deviation for eighth graders on the examination is less than 29. At $\alpha$ = 0.10, is there enough evidence to support the administrator's claim?

Ever improving technologies have led to the development of better alloys. Similar research was carried out to explore better ways of manufacturing gasoline or diesel-powered engine blocks. Researchers developed a manufacturing methodology using compacted graphite cast iron (CGI) and magnesium alloy AMC-SCI. Assume that 50 tests have been conducted on each of these two alloys in similar conditions for recording their melting points in Fahrenheit. Assume that the average melting point for CGI has been recorded as 236 with a variance of 25. The average melting point recorded for AMC-SCI was 224 with a variance of 15 in all the 50 tests conducted. Answer the following questions, assuming that the population variances are equal.

a. Construct the confidence intervals at 90% for the population mean for CGI.

b. Construct the confidence intervals at 95% for the mean difference between engine blocks using the two alloys.

c. At 0.05 level of significance, test the hypothesis that the average melting point using CGI is greater than the average melting point using AMC-SCI. In other words, test the hypothesis of the difference in the melting points of the two alloys.

d. Calculate p-value and interpret the results in (b) and (c).

For simplicity, suppose there are five students in a class. Suppose the scores of these students on three tests are as follows:

$$\begin{array}{cccc} \hline \text { Student } & \text { Test 1 } & \text { Test 2 } & \text { Test 3 } \\ \hline A & 80 & 84 & 92 \\ \hline B & 84 & 86 & 88 \\ \hline C & 78 & 76 & 82 \\ \hline D & 86 & 82 & 78 \\ \hline E & 92 & 94 & 88 \\ \hline \end{array}$$

a. Write a $5 \times 3$ matrix $A$ to represent the information.

b. What are $a_{11}, a_{12}$, and $a_{13}$ ? What is $\frac{1}{3}\left(a_{11}+a_{12}+a_{13}\right)$, and what does this quantity represent?

c. What are $a_{12}, a_{22}, a_{32}, a_{42}$, and $a_{52}$ ? What is $\frac{1}{5}\left(a_{12}+a_{22}+a_{32}+a_{42}+a_{52}\right)$, and what does this quantity represent?

d. What is the average score of student $E$ based on the three tests?

e. What is the average score of the five students for the third test?

1. The class boxType is defined by extending the definition of the class rectangleType. In this exercise, derive the class boxType from the class rectangleType, add the functions to overload the operators +, -, *, ==, !=, <=, <, >=, >, and pre- and post-increment and decrement operators as members of the class boxType. Also overload the operators << and >>. Overload the relational operators by considering the volume of the boxes. For example, two boxes are the same if they have the same volume.

2. Write the definitions of the functions of the class boxType as defined in part (1).

3. Write a test program that tests various operations on the class rectangleType.