True or False Questions

If the unit cost remains constant, there is no difference in the value of stock among actual cost, FIFO, LIFO, and weighted average cost methods.?

LIFO is often expressly prohibited, especially when it would artificially reduce tax liabilities.?

Consolidating is the process where small loads from different suppliers are combined to give full vehicle loads for delivery to customers?

The main problems with quantitative forecasts are subjective views and are not as reliable as quantitative methods.?

We should keep an outlier if we can explain the reasons behind it.?

Coefficient of correlation can range from −∞ ??+∞.?

The parameters in exponential smoothing are selected to minimize the sum of errors.?

On a plot of forecast errors, a trend line signals there is a trend not accounted for in the forecast model?

Customers arrive in a certain shop according to an approximate Poissonprocess on the average of two every 6 minutes.

(a) Using the Poisson distribution calculate the probability of two or more customersarrive in a 2-minute period.

(b) Consider X denote number of customers and X follows binomial distribution withparametersn= 100. Using the binomial distribution calculate the probability oftwo or more customers arrive in a 2-minute period.

(c) Let Y denote the waiting time in minutes until the first customer arrives. (i) Whatis the pdf ofY? (ii) Findq1=π0.75

(d) Let Y denote the waiting time in minutes until the first customer arrives. What isthe probability that the shopkeeper will have to wait more than 3 minutes for thearrival of the first customer ?

(e) What is the probability that shopkeeper will wait more than 3 minutes before bothof the first two customers arrive?

2. The long-term graduation rate for female athletes at a certain midwestern university is 72%. A random sample of female athletes at this school over the past few years showed that 29 of 35 females athletes graduated.

   (a) (10 pts) Test to determine if the proportion of female athletes who graduate from this school is greater than 72% at the 0.05 level of significance.

   (b) (5 pts) Suppose that a Type I error was made in the hypothesis test in part (a). Explain what a Type I error would be in the context of this problem. What is the probability of committing a Type I error in this problem?

Determine the critical value for a right-tailed test regarding a population propotion at the alpha = 0.05 level of signficiance

z=

A scientist is studying the relationship between x = inches of annual rainfall and y = inches of shoreline erosion. One study reported the following data. Use the following information to solve the problem by hand, then use SPSS output to verify your answers. .

X         30        25        90        60        50        35       75        110      45        80

Y         0.3       0.2       5.0       3.0       2.0       0.5       4.0       6.0       1.5       4.0

a. What is the equation of the estimated regression line?

= ______________

b. Plot the data and graph the line. Does the line appear to provide a good fit to the data points?

c. Use the least-squares line to predict the value of y when x =39

d. Fill in the missing entries in the SPSS analysis of variance table

Source             DF                   SS                    MS                  F                      P

Regression       1                      37.938

Error                ____                _____              0.058               ____________

e) Is the simple linear regression model useful for predicting erosion from a given amount of rainfall?

f) What is the p-value?

g) A linear relationship ______________ exist between x and y.

h) The simple linear regression model ______________ useful for predicting erosion from a given amount of rainfall.

i) What is the coefficient of determination.(r-squared) or r?

j) Interpret the coefficient (r-squared) of determination.

Women athletes at the a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 40 women athletes at the school showed that 21 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 1% level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p < 0.67; H₁: p = 0.67H₀: p = 0.67; H₁: p > 0.67    H₀: p = 0.67; H₁: p ≠ 0.67H₀: p = 0.67; H₁: p < 0.67

(b) What sampling distribution will you use?

The standard normal, since np > 5 and nq > 5.The Student's t, since np > 5 and nq > 5.    The Student's t, since np < 5 and nq < 5.The standard normal, since np < 5 and nq < 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)


(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

Multiple choice problem:

Question:

Munchies Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 milligrams of vitamin A and 12 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 8 mg of vitamin A and 1 mg of vitamin B, whereas an ounce of rice contributes 6 mg of A and 2 mg of B. An ounce of oats costs $0.05 and an ounce of rice costs $0.03. The linear optimization model is: Minimize Total Cost 8x1 + 6x2 ≥ 48 1x1 + 2x2 ≥ 12 x1, x2 ≥ 0 Solve this model using Solver. Which variables are positive in the optimal solution?

Multiple choice answer options (only one answer is correct. Either A, B, C or D):

A.) Both oats and rice are zero

B.) Only rice

C.) Only oats

D.) Both oats and rice

what does the operation "recode into different variables" do to data in spss

Suppose Jamal is studying poverty in his economics class, and he wants to compare the proportion of individuals living below the poverty line in the western United States in different years. He collects data on a simple random sample of people from 2013 and a simple random sample of people from 2014. His data are summarized in the table.

Jamal wants to run a two-sample z‑test for the difference of two proportions to test the alternative hypothesis, H1:p1>p2, against the null hypothesis, H0:p1=p2, where p1 is the proportion of population in 2013 that are living below the poverty line, and p2 is the proportion of population in 2014 that are living below the poverty line. Jamal selects a significance level of α=0.10.

Compute the z‑statistic and P-value for Jamal’s z‑test for the difference of two proportions, p1−p2. Give your answers precise to three decimal places.

Based on your answers and a significance level of α=0.10, complete the following sentences to state the decision and conclusion of Jamal’s test.

Source: adapted from DeNavas-Walt, Carmen and Bernadette D. Proctor. Income and Poverty in the United States: 2014. Table 3. People in Poverty by Selected Characteristics: 2013 and 2014 [Online]; U.S. Census Bureau, Current Population Reports: U.S. Government Printing Office, Washington, DC, 2015; P60-252. https://www.census.gov/content/dam/Census/library/publications/2015/demo/p60-252.pdf (accessed September 11, 2016).

Jamal decides                                                                           the                                                                          

hypothesis. The conclusion is that                                                                            the proportion of the 2013 population

living in poverty                                                                           the proportion of the 2014 population living in

poverty, because                                                                             .

Answer Bank

compared to

is the same as

that no decision can be made about

no conclusion can be drawn about

alternative

null

the test requirements have not been met

there is sufficient evidence that

to reject

to fail to reject

there is insufficient evidence that

is higher than

the difference is statistically significant (P<0.10)

is different than

the difference is not statistically significant (P>0.10)

is less than

accept

The success rate of corneal transplant surgery is 85%. The surgery is performed on six patients.

1. Construct a binomial distribution.
2. Graph the binomial distribution using a histogram and describe its shape.
3. Find the mean, variance, and standard deviation of the binomial distribution and interpret the results.

A company claimed that every​ 18-ounce bag of their chocolate chip cookies contained at least 1000 chocolate chips. Dedicated statistics students at a school purchased some randomly selected bags of cookies and counted the chocolate chips. Some of their data are given below. ​

1123 1127 1094 1206 1406 1109 1310 1332 1259 1263 1354 1142 1186 1276 1291 1139

a) Check the assumptions and conditions for inference. Comment on any concerns you have. ​

The independence condition ____ satisfied and the Nearly Normal Condition ____ satisfied.​ Therefore, using the​ Student-t model for inference ___ reliable.

b) Test their claim by performing an appropriate hypothesis test.

Bag 1 contains 3 red balls and 7 green balls. Bag 2 contains 8 red balls and 4 green balls. Bag 3 contains 5 red balls and 11 green balls. Bag 1 is chosen twice as often as either Bag 2 or Bag 3 (which have the same probability of being chosen). After a bag is chosen, a ball is chosen at random from that bag. Calculate the probability that:

a) a red ball is chosen

b) a red ball from Bag 2 is chosen

c) if it is known that a red ball is chosen, what is the probability that it comes from Bag 2?

1. You and a group of friends wish to start a company. You have an idea, and you are comparing startup incubators to apply to. (Startup incubators hold classes and help startups to contact venture capitalists and network with one another) Assume funding is normally distributed.

Incubator A has an 80% success ratio getting companies to survive at least 4 years from inception. The average venture funding of the 28 companies reaching that 4-year mark, is 1.3 million dollars with a standard deviation of 0.6 million

Incubator B has a 60% success ratio getting companies to survive at least 4 years from inception. The average venture funding of the 21 companies reaching that 4-year mark, is 1.9 million dollars with a standard deviation of 0.55 million

a. Are the success ratios significantly different? (note the count is given but not N, how do you find N?)

b. Is the average funding in incubator B significantly different from the average funding in a? (use a=0.01). Assume a normal distribution

Two professors at a local college developed a new teaching curriculum designed to increase​ students' grades in math classes. In a typical developmental math​ course, 53​% of the students complete the course with a letter grade of​ A, B, or C. In the experimental​ course, of the 14 students​ enrolled, 11 completed the course with a letter grade of​ A, B, or C. Is the experimental course effective at the alpha equals 0.01 level of​ significance? Complete parts ​(a) through​ (g).

​(a) State the appropriate null and alternative hypotheses.

​(b) Verify that the normal model may not be used to estimate the​ P-value.

​(c) Explain why this is a binomial experiment

(d) Determine the​ P-value using the binomial probability distribution. State your conclusion to the hypothesis test.

​(e) Suppose the course is taught with 4242 students and 3333 complete the course with a letter grade of​ A, B, or C. Verify whether the normal model may now be used to estimate the​ P-value

(f) Use the normal model to obtain and interpret the​ P-value. State your conclusion to the hypothesis test.

(g) Explain the role that sample size plays in the ability to reject statements in the null hypothesis.