Calculate the amount of solution (g or mL) that contains each of the following amounts of solute.

5.2 g of LiNO3 from a 35 %(m/m) LiNO3 solution.

31.6 g of KOH from a 20.0 %(m/m) KOH solution.

3.1 mL of formic acid from a 18 %(v/v) formic acid solution.

A wheel of radius b is rolling along a muddy road with a speed v. Particles of mud attached to the wheel are being continuously thrown off from all points of the wheel. If v2 > 2bg, where g is the acceleration of gravity, find the maximum height above the road attained by the mud, H = H(b,v,g).

The drag force on a large ball that weighs 200 g in free flight is given by FD = 2*10 V , where FD is in Newtons and V is in meters per second. If the ball is dropped from rest 300 m above the ground, determine the speed at which it hits the ground. What percentage of the terminal speed is the result?

We sampled a group of undergraduate students (n=1200) to determine the proportion of students who were considered binge drinkers. We hypothesized that the proportion of students who were binge drinkers were less than the national proportion of college students who were binge drinkers (pnull=0.35).

1. What are the appropriate null and alternative hypotheses?

2. Among the 1200 students sampled, the proportion of binge drinkers (p^) was 0.27. With a one sample z-test, our calculated z was -5.67 and the theoretical z was -1.645. With an alpha of 0.05, we:

a. do no have enough evidence to suggest that the proportion of binge drinkers is less than the national average.

b. have statistically significant evidence to show that the proportion of students who are binge drinkers is less than the national proportion of students are binge drinkers

c. we do not have enough information.

3. We calculated a 95% CI around the sample proportion. The 95% CI is (.247, .293). Based on the CI, we can

a. reject the null hypothesis

b. fail to reject the null hypothesis

c. this cannot be determined based on info given

Suppose the chance of getting flu is independent of each other. Suppose 20% of graduate school students nationwide develop influenza. Further, suppose we have a class of size 15. Let X be the number of students who get flu, calculate the following probabilities:

1. Exactly 4 get influenza. Which is the correct answer? There might be slight rounding differences. Please provide an explanation.

a. 0.500

b. 0.188

c. 0.123

d. 0.818

2. No more than 4 get influenza. Which is the correct answer? There might be slight rounding differences. Please provide an explanation.

a. 0.500

b. 0.836

c. 0.001

d. 0.368

3. Less than 4 get influenza. Which is the correct answer? There might be slight rounding differences. Please provide an explanation.  

a. 0.648

b. 0.846

c. 0.125

d. 0.684

4. How many students should the teacher expect to be sick with influenza that year? Which is the correct answer? The answer is NOT 3 students. There might be slight rounding differences. Please provide an explanation.

a. 2 students

b. 5 students

c. 1 student

d. 4 students

For each of the following three cases, explain (i) the hypotheses with a plausible definition of p1 and p2, (ii) whether or not the data indicate practical significance (use common sense and/or general knowledge), and (iii) whether or not the data indicate statistical significance. (a) A recent study of perfect pitch tested 2,700 students in American music conservatories. It found that 7% of non-Asian students and 32% of Asian students have perfect pitch. A two-sample Z-test of the difference in proportions resulted in a p-value of < 0.0001. (b) In July 1974, the PEW Research Center selected a large sample of voters. Sixty-six percent of those interviewed disapproved of President Nixon. In July 2007, the same PEW Research Center selected a comparable sample. In this case, 64.5% of those interviewed expressed disapproval of President Bush. The researchers pointed out that the p-value for comparing the two sample results was 0.023. (c) In a survey conducted in a statistics class at Boston College, students were asked their views on a number of social issues; 56% of the male students and 38% of the female students supported the death penalty. In a statistics lab, the students computed the corresponding p-value as 0.21.

A student group claims that first-year students at a university should study 2.5 hours (150 minutes) per night during the school week. A skeptic suspects that they study less than that on the average. A survey of 51 randomly selected students finds that on average students study 138 minutes per night with a standard deviation of 32 minutes. What conclusion can be made from this data? Select one:

A) The p-value is greater than .05, therefore we do not have enough evidence to conclude that students study less than 150 minutes per night.

B) The p-value is less than .05, therefore we conclude that students study greater than 150 minutes per night.

C) The p-value is less than .05, therefore we conclude that students study less than 150 minutes per night.

D) We do not have enough information to make a conclusion about this study. The p-value is less than .05, therefore we do not have enough evidence to conclude that students study less than 150 minutes per night.

The following 14 questions (Q78 to Q91) are based on the following example:

A researcher wants to determine whether high school students who attend an SAT preparation course score significantly different on the SAT than students who do not attend the preparation course. For those who do not attend the course, the population mean is 1050 (μ = 1050). The 16 students who attend the preparation course average 1150 on the SAT, with a sample standard deviation of 300. On the basis of these data, can the researcher conclude that the preparation course has a significant difference on SAT scores? Set alpha equal to .05.

Q78: The appropriate statistical procedure for this example would be a

• A. z-test
• B. t-test

Q79: Is this a one-tailed or a two-tailed test?

• A. one-tailed
• B. two-tailed

Q80: The most appropriate null hypothesis (in words) would be

• A. There is no statistical difference in SAT scores when comparing students who took the SAT prep course with the general population of students who did not take the SAT prep course.
• B. There is a statistical difference in SAT scores when comparing students who took the SAT prep course with the general population of students who did not take the SAT prep course.
• C. The students who took the SAT prep course did not score significantly higher on the SAT when compared to the general population of students who did not take the SAT prep course.
• D. The students who took the SAT prep course did score significantly higher on the SAT when compared to the general population of students who did not take the SAT prep course.

Q81: The most appropriate null hypothesis (in symbols) would be

• A. μ_SATprep = 1050
• B. μ_SATprep = 1150
• C. μ_SATprep 1050
• D. μ_SATprep 1050

Q82: Set up the criteria for making a decision. That is, find the critical value using an

alpha = .05. (Make sure you are sign specific: + ; - ; or ) (Use your tables)

Summarize the data into the appropriate test statistic.

Steps:

Q83: What is the numeric value of your standard error?

Q84: What is the z-value or t-value you obtained (your test statistic)?

Q85: Based on your results (and comparing your Q84 and Q82 answers) would you

• A. reject the null hypothesis
• B. fail to reject the null hypothesis

Q86: The best conclusion for this example would be

• A. There is no statistical difference in SAT scores when comparing students who took the SAT prep course with the general population of students who did not take the SAT prep course.
• B. There is a statistical difference in SAT scores when comparing students who took the SAT prep course with the general population of students who did not take the SAT prep course.
• C. The students who took the SAT prep course did not score significantly higher on the SAT when compared to the general population of students who did not take the SAT prep course.
• D. The students who took the SAT prep course did score significantly higher on the SAT when compared to the general population of students who did not take the SAT prep course.

Q87: Based on your evaluation of the null in Q85 and your conclusion is Q86, as a researcher you would be more concerned with a

• A. Type I statistical error
• B. Type II statistical error

Calculate the 99% confidence interval.

Steps:

Q88: The mean you will use for this calculation is

• A. 1050
• B. 1150

Q89: What is the new critical value you will use for this calculation?

Q90: As you know, two values will be required to complete the following equation:

__________ __________

Q91: Which of the following is a more accurate interpretation of the confidence interval you just computed?

• A. We are 99% confident that the scores fall in the interval _____ to _____.
• B. We are 99% confident that the average score on the SAT by the students who took the prep course falls in the interval _____ to _____.
• C. We are 99% confident that the example above has correct values.
• D. We are 99% confident that the difference in SAT scores between the students who took the prep course and the students who did not falls in the interval _____ to _____.

1. This question takes you through the design-based approach to sorting out sampling
distributions, their means and variances, and the estimation of these quantities when
you sample with and without replacement.
Consider a population of 5 individuals. The variable is their annual income in 1000s
of dollars per year, and you want to estimate the population mean income based on
a random sample of size two. The values of income are as follows:
Individual Income
A 80
B 18
C 24
D 52
E 24

(a) Make a list of all the samples of size 2 possible without replacement. Find the
sample mean and sample variance of each of these samples using the formula

yS = 1/n sigma yi

s^2 = 1/(n-1) sigma(yi - y(average))^2

(b) Find the sampling distributions of the sample mean and sample standard devi-
ation based on (a).
(c) Find the expected values of the sampling distributions of by using

E[W] = sigma wP[W = w]

(d) Find the variance of the sampling distribution of by using
V [W] =sigma (w - E[W])2P[W = w]
(e) Compare the results from (c) and (d) with the population mean, the population
variance as calculated from
S^2 = 1/(N-1) sigma (yi - yU)^2
and the variance of the sampling distribution of as calculated from
V [y] = S2/n(1 -n/N)

(f) For sampling with replacement, nd the sampling distribution of the sample
mean by listing all the samples that can occur, nding the sample mean values
for each sample, and nding the probability that each value occurs. Be careful:
in one kind of sampling, the order in which the individuals are sampled can't
be ignored.