Consider the cell described below at 291 K:

Sn | Sn²⁺ (0.753 M) || Pb²⁺ (0.921 M) | Pb

Given E^o_Pb²⁺→Pb = -0.131 V, E^o_Sn²⁺→Sn = -0.143 V. Calculate the cell potential after the reaction has operated long enough for the Sn²⁺ to have changed by 0.325 mol/L.

Design an O(n log n) algorithm that takes two arrays A and B (not necessarily sorted) of size n of real numbers and a value v. The algorithm returns i and j if there exist i and j such that A[i] + B[j] = v and no otherwise. Describe your algorithm in English and give its time analysis.

A statistics professor asked her students whether or not they were registered to vote. In a sample of 50 of her students (randomly sampled from her 700 students), 35 said they were registered to vote.

Questions 1 - 6 pertain to scenario 1.

Question 1 (1 point)

Which of the following properly explains the 95% confidence interval for the true proportion of the professor's students who were registered to vote?

Question 1 options:

Question 2 (1 point)

Explain what 95% confidence means in this context.

Question 2 options:

Question 3 (1 point)

What would your response be if you were asked by a non-statistical student about the probability that the true proportion of the professor's students who were registered to vote is in your confidence interval?

Question 3 options:

Question 4 (1 point)

According to a Gallup poll, about 73% of 18- to 29-year-olds said that they were registered to vote. How would you interpret the Gallup poll's result?

Question 4 options:

Question 5 (1 point)

If the professor only knew the information from the Gallup poll and wanted to estimate the percentage of her students who were registered to vote to within ±4% with 95% confidence, what approach would she use to determine how many students she should sample?

Question 5 options:

Question 6 (1 point)

Suppose the professor wanted to make the margin of error smaller. What would accomplish this?

Question 6 options:

Sleep – College Students: Suppose you perform a study about the hours of sleep that college students get. You know that for all people, the average is about 7 hours. You randomly select 50 college students and survey them on their sleep habits. From this sample, the mean number of hours of sleep is found to be 6.2 hours with a standard deviation of 0.86hours. We want to construct a 95% confidence interval for the mean nightly hours of sleep for all college students.
(a) What is the point estimate for the mean nightly hours of sleep for all college students?
? hours
(b) What is the critical value of t (denoted t_α/2) for a 95% confidence interval? Use the value from the table or, if using software, round to 3 decimal places.
t_α/2 =  
(c) What is the margin of error (E) for a 95% confidence interval? Round your answer to 2 decimal places.
E = ? hours
(d) Construct the 95% confidence interval for the mean nightly hours of sleep for all college students. Round your answers to 1 decimal place.
? < μ < ?

(e) Based on your answer to (d), are you 95% confident that the mean nightly hours of sleep for all college students is below the average for all people of 7 hours per night? Why or why not?

Yes, because 7 is above the upper limit of the confidence interval for college students.

No, because 7 is below the upper limit of the confidence interval for college students.  

  Yes, because 7 is below the upper limit of the confidence interval for college students.

No, because 7 is above the upper limit of the confidence interval for college students.
(f) We are never told whether or not the parent population is normally distributed. Why could we use the above method to find the confidence interval?

Because the sample size is less than 100.

Because the margin of error is less than 30.    

Because the sample size is greater than 30.

Because the margin of error is positive.

Researchers are always looking for methods to help students improve their mathematics test scores. A company recently announced that they have found a way to help college students complete a certain mathematics test more quickly. The company said that using a specific meditation method for 20 minutes, before taking a mathematics test, would help students complete the test more quickly. Researchers have done studies, with thousands of general college students, to see how long it takes them (in minutes) to complete the mathematics test. The results follow a normal distribution with a mean of 70 minutes and standard deviation of 4 minutes. A mathematics researcher wants to use a statistical test to decide if the meditation method is believable. That is, will it actually help students complete the test more quickly? Researcher conduct a hypothesis with 100 college students who complete the test after meditating for 20 minutes to determine if students who meditate before the test are able to complete the mathematics test more quickly than normal.

4. Which of the following pairs represent appropriate hypotheses for this problem?

a. H0: µ = 70, Ha: µ > 70

b. H0: µ = 20, Ha: µ < 20

c. H0: µ = 20, Ha: µ > 20

d. H0: µ = 70, Ha: µ < 70

5. Using a representative sample, the researcher found that a sample of college students who meditated before the test had a mean time of x ̅=60.5 minutes and a P-value of less than 0.001. What could she (the researcher) conclude for this result at the 1% significance level?

a. The researcher has statistical evidence that, for college students, meditation improves the time it takes to complete the test.

b. The researcher has proven that, for college students, meditation substantially improves the time it takes to complete the test.

c. The researcher does not have enough evidence to say that, for college students, meditation substantially improves the time it takes to complete the test.

A class survey in a large class for first‑year college students asked, “About how many hours do you study during a typical week?” The mean response of the 463 students was ?¯=13.7 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation ?=7.4 hours in the population of all first‑year students at this university.

Regard these students as an SRS from the population of all first‑year students at this university. Does the study give good evidence that students claim to study more than 13 hours per week on the average?

You may find Table A helpful.

(a) State null and alternative hypotheses in terms of the mean study time in hours for the population.

A. ?0:?=13 hours ; ??:?=13 hours

B. ?0:?=13 hours ; ??:?≠13 hours

C. ?0:?=13 hours ; ??:?<13 hours

D. ?0:?=13 hours ; ??:?>13 hours

(b) What is the value of the test statistic ? ? (Enter your answer rounded to two decimal places.)

?=

(c) What is the ? ‑value of the test?

A. between 0.001 and 0.005

B. less than 0.0001

C. larger than 0.05

D. between 0.020 and 0.030

(d).Can you conclude that students do claim to study more than 13 hours per week on average?

A. No, the small ? ‑value is strong evidence that students do not claim to study more than 13 hours per week on average.

B. No, the large ? ‑value is strong evidence that students do not claim to study more than 13 hours per week on average.

C. Yes, the large ? ‑value is strong evidence that students do claim to study more than 13 hours per week on average.

D. Yes, the small ? ‑value is strong evidence that students do claim to study more than 13 hours per week on average.

1- Which of the following is NOT considered an area covered by learning styles?

2- Due to the lack of empirical support, a more appropriate name for learning styles would be learning __________.

3- Research supports the idea that most students retain more information using __________ approaches to teaching.

4- Relying in rote (maintenance) rehearsal leads to __________ processing of the information.

5- Despite the lack of research evidence, the concept of learning styles remains popular for which reason(s) below?

6- According to the National Center for Educational Statistics, which type of disability below is the most prevalent?

7- A __________ limits your ability to do something specific, whereas a __________ limits your ability to do something regardless of the situation.

8- One of the benefits of labeling students is that it...

9- Which of the following laws, acts, or subsections established the need for students with disabilities to have Individualized Education Programs (IEPs)?

Exercises

1. A 25 kVA single-phase transformer has the primary and secondary number of turns of 200 and 400, respectively. The transformer is connected to a 220 V, 50 Hz source. Calculate the (i) turns ratio, and (ii) mutual flux in the core.

2. A 25 kVA, 2200/220 V, 50 Hz single-phase transformer’s low voltage side is short-circuited and the test data recorded from the high voltage side are P=150 W, I1 = 5A and V1 = 40 V. Determine the (i) equivalent resistance, reactance and impedance referred to primary, (ii) equivalent resistance, reactance and impedance referred to secondary.

3. A 30 kVA transformer has the iron loss and full load copper loss of 350 and 650 W, respectively. Determine the (i) full load efficiency, (ii) output kVA corresponding to maximum efficiency, and (iii) maximum efficiency. Consider that the power factor of the load is 0.6 lagging. (97.74%, 13.2 kW, 94.96%).

4. A 2.5 kVA, 200 V/40 V single-phase transformer has the primary resistance and reactance of 3 and 12 Ω, respectively. On the secondary side, these values are 0.3 and 0.1 Ω, respectively. Find the equivalent impedance referred to the primary and the secondary. (17.9ohms, 0.72ohms).

Synthetically produced ethanol is an important industrial commodity used for various purposes, including as a solvent (especially for substances intended for human contact or consumption); in coatings, inks, and personal care products; for sterilization; and as a fuel. Industrial ethanol is a petrochemical synthesized by the hydrolysis of ethylene:

C2H4 (g) + H2O (v) <=>C2H5OH (v)
Some of the product is converted to diethyl ether in the undesired side reaction:

2 C2H5OH (v)<=> (C2H5 )2O (v) + H2O (v)

The combined feed to the reactor contains 53.7 mole% C2H4, 36.7% H2O, and the balance nitrogen, and enters the reactor at 310oC. The reactor operates isothermally at 310oC. An ethylene conversion of 5% is achieved, and the yield of ethanol (moles ethanol produced/moles ethylene consumed) is 0.900. Hint: treat the reactor as an open system.

Data for Diethyl Ether:

ˆ
H of = -271.2 kJ/mol for the liquid

ˆ
Hv = 26.05 kJ/mol (assume independent of T )

Cp[kJ/(molC)] = 0.08945 + 40.33*10-5T(C) -2.244*10-7T2

(a) Calculate the reactor heating or cooling requirement in kJ/mol feed.
(b) Why would the reactor be designed to yield such a low conversion of ethylene? What processing

step (or steps) would probably follow the reactor in a commercial implementation of this process?