Eric wants to estimate the percentage of elementary school children who have a social media account. He surveys 500 elementary school children and finds that 250 have a social media account. Identify the values needed to calculate a confidence interval at the 99% confidence level. Then find the confidence interval.

It is estimated that 16% of those taking the quantitative methods portion of the certified public accountant (CPA) examination fail that section. Seventy students are taking the examination this Saturday.

a-1. How many would you expect to fail? (Round the final answer to 2 decimal places.)

Number of students           

a-2. What is the standard deviation? (Round the final answer to 2 decimal places.)

Standard deviation           

b. What is the probability that exactly eight students will fail? (Round the final answer to 4 decimal places.)

Probability           

c. What is the probability at least eight students will fail? (Round the final answer to 4 decimal places.)

Probability           

A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325​-mg upper limit set by regulations for​ "reduced sodium" franks. The mean sodium content for the sample was 321.9 mg with a standard deviation of 19 mg. Assume that the assumptions and conditions for the test are met.

The test statistic is t = _

​(Round to two decimal places as​ needed.)

The​ P-value is _

​(Round to three decimal places as​ needed.)

Given data from a completely randomized design experiment:

Treatment 1 = {3.8, 1.2, 4.1, 5.5, 2.3}

Treatment 2 = {5.4, 2.0, 4.8, 3.8}

Treatment 3 = {1.3, 0.7, 2.2}

a.) Calculate the treatment means and variances for each of the 3 treatments above.

b.) Use statistical software to complete the ANOVA table.

c.) In words, what is the null and alternative hypotheses for the ANOVA F-test?

d.) Test the null hypothesis that µ1=µ2=µ3against the alternative hypothesis that at least two means differ. Use α = .01.

e.) Explain in words what the ANOVA test tells us about the equality of treatment means?

Let X be a continuous random variable with pdf: f(x) = ax^2 − 2ax, 0 ≤ x ≤ 2

(a) What should a be in order for this to be a legitimate p.d.f?

(b) What is the distribution function (c.d.f.) for X?

(c) What is Pr(0 ≤ X < 1)? Pr(X > 0.5)? Pr(X > 3)?

(d) What is the 90th percentile value of this distribution? (Note: If you do this problem correctly, you will end up with a cubic equation that you need to solve. You may solve it numerically.)

(e) What are the mean and variance of this distribution?

6.4 You are an environmental regulator in a developed country faced with a decision as to whether to permit mining in a wetland’s wilderness are that probably contains threatened species. You are required to perform an assessment of the desirability of this activity.

a) What should your opinion set be?

b) Perform a CPSA for each opinion (this can be qualitative). What stakeholders should you involve in order to support your CPSAs? What are the major issues that can be resolved by gathering data, and what issues involve value judgments?

c) Are there any issues you feel are important, but you cannot fit into a CPSA? Assuming that there are, how would you ensure they are considered as part of the regulatory process?

Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store’s leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 10% higher than the market price the distributor pays for the beans. The current market price is $0.46 per pound for Brazilian Natural and $0.64 per pound for Colombian Mild. The compositions of each coffee blend are as follows: Blend Bean Regular DeCaf Brazilian Natural 60% 40% Colombian Mild 40% 60% Romans sells the Regular blend for $3.1 per pound and the DeCaf blend for $4.3 per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the production of 1050 pounds of Romans Regular coffee and 500 pounds of Romans DeCaf coffee. The production cost is $0.8 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.15 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit. Let BR = pounds of Brazilian beans purchased to produce Regular BD = pounds of Brazilian beans purchased to produce DeCaf CR = pounds of Colombian beans purchased to produce Regular CD = pounds of Colombian beans purchased to produce DeCaf If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a plus sign before the blank. (Example: -300) The complete linear program is

1. Max	BR	+	BD	+	CR	+	CD
   s.t.
   Regular Blend	BR			+	CR			=
   DeCaf blend			BD			+	CD	=
   Regular production	BR				CR			=
   DeCaf production			BD			+	CD	=
   BR, BD, CR, CD ≥ 0

   What is the optimal solution and what is the contribution to profit? If required, round your answer to the nearest whole number.

   Optimal solution:

   BR =

   BD =

   CR =

   CD =

   If required, round your answer to the nearest cent.

   Value of the optimal solution = $  

Suppose x has a normal distribution with mean μ = 36 and standard deviation σ = 5.

Describe the distribution of x values for sample size n = 4. (Round σ_x to two decimal places.)

Describe the distribution of x values for sample size n = 16. (Round σ_x to two decimal places.)

Describe the distribution of x values for sample size n = 100. (Round σ_x to two decimal places.)

A professor states that in the United States the proportion of college students who own iPhones is .66. She then splits the class into two groups: Group 1 with students whose last name begins with A-K and Group 2 with students whose last name begins with L-Z. She then asks each group to count how many in that group own iPhones and to calculate the group proportion of iPhone ownership. For Group 1 the proportion is p1 and for Group 2 the proportion is p2. To calculate the proportion you take the number of iPhone owners and divide by the total number of students in the group. You will get a number between 0 and 1.

• What would you expect p1 and p2 to be?
• Do you expect either of these proportions to be vastly different from the population proportion of .66?
• Would you be surprised if p1 was different than p2?
• Would you be surprised if they were the same or similar?
• What statistical concept describes the relationship between the first letter of someone's last name and whether or not they own an iPhone?

According to the M&M^® website, the average percentage of brown M&M^® candies in a package of milk chocolate M&Ms is 14%. (This percentage varies, however, among the different types of packaged M&Ms.) Suppose you randomly select a package of milk chocolate M&Ms that contains 57 candies and determine the proportion of brown candies in the package.

(b) What is the probability that the sample proportion of brown candies is less than 25%? (Round your answer to four decimal places.)


(c) What is the probability that the sample proportion exceeds 33%? (Round your answer to four decimal places.)


(d) Within what range would you expect the sample proportion to lie about 95% of the time? (Round your answers to two decimal places.)

lower limit:

upper limit:

Female undergraduates in randomized groups of 14 took part in a self-esteem study. The study measured an index of self-esteem from the point of view of competence, social acceptance, and physical attractiveness. Let x₁, x₂, and x₃ be random variables representing the measure of self-esteem through x₁ (competence), x₂ (social acceptance), and x₃ (attractiveness). Higher index values mean a more positive influence on self-esteem.

(a) Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

(b) Find a 99% confidence interval for μ₁ − μ₃. (Round your answers to two decimal places.)

(c) Find a 99% confidence interval for μ₂ − μ₃. (Round your answers to two decimal places.)

In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 473 eggs in group I boxes, of which a field count showed about 278 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 796 eggs in group II boxes, of which a field count showed about 270 hatched.

(d) Find a 95% confidence interval for p₁ − p₂. (Round your answers to three decimal places.)

Please Use R studio to answer the question. This is the Statistics section of Comparing Groups.

One month before the election, a poll of 630 randomly selected votes showed 54% planning to vote for a certain candidate. A week later, it became known that he had had an extramarital affair, and a new poll showed only 51% of 1010 voters supporting him. Do these results indicate a decrease in voter support fo his candidacy?

a) Test an appropriate hypothesis as state your conclusion.

b) If you concluded there was a difference, estimate that difference with a confidence interval and interpret your interval in context.

2. A jar contains 5 balls, 4 of which are blue and one red.

(a) If you draw balls one at a time and replace them, what is the expected draw at which

you will see the red ball?

(b) If you draw balls one at a time, but without replacing them, what is the expected time

to see the red ball?

3. A jar contains 1 red ball and an unknown number of blue balls. You make 20 draws with

replacement from the jar. What is a maximum likelihood estimator of the number of blue

balls in the jar?

About 42.3% of Californians speak a language other than English at home. Using your class as the sample, conduct a hypothesis test to determine if the percent of students at school that speak a language other than English at home is different from 42.3%. 23 out of 34 students in the sample speak a language other than English at home

a. State the distribution to use for the test. If t, include the degrees of freedom. If normal, include the mean and standard deviation.

b. p-value = ______________

c. reject the null hypothesis or do not reject the null hypothesis

The population of weights for men attending a local health club is normally distributed with a mean of 173-lbs and a standard deviation of 30-lbs. An elevator in the health club is limited to 35 occupants, but it will be overloaded if the total weight is in excess of 6615-lbs. Assume that there are 35 men in the elevator. What is the average weight of the 35 men beyond which the elevator would be considered overloaded? average weight = lbs What is the probability that one randomly selected male health club member will exceed this weight? P(one man exceeds) = (Report answer accurate to 4 decimal places.) If we assume that 35 male occupants in the elevator are the result of a random selection, find the probability that the elevator will be overloaded? P(elevator overloaded) = (Report answer accurate to 4 decimal places.) If the elevator is full (on average) 5 times a day, how many times will the elevator be overloaded in one (non-leap) year? number of times overloaded = (Report answer rounded to the nearest whole number.)