In the EAI sampling problem, the population mean is $51,800 and the population standard deviation is $4,000. When the sample size is n = 20, there is a 0.4246 probability of obtaining a sample mean within +/-$500 of the population mean. Use z-table.

a. What is the probability that the sample mean is within $500 of the population mean if a sample of size 40 is used (to 4 decimals)?

b. What is the probability that the sample mean is within $500 of the population mean if a sample of size 80 is used (to 4 decimals)?

It is known that the thread life of a certain type of tire has a normal distribution with standard deviation of 1500.

a) A sample of 16 tires is found to have an average thread life of 30960. Does this provide sufficient evidence at 1% level of significance to conclude that the true average thread life of this type of tires is more than 30000? Explain by carrying out an appropriate hypothesis test stating clearly the hypotheses.

b) What is the probability of making a Type II error in the hypothesis test in part "a" if the true average thread life is in fact 31000?

c) If a 1% level of significance is used to carry out the test in part "a" and it is also required that ?(30500) = 0.05, what sample size is necessary?

THE ANSWERS ARE AS FOLLOWS

a) ?=30000, ?>30000, z=2.56, z0.01=2.327, reject.

b) 0.3671

c) 142

Please explain the process to solve this problem. Thank you!

Your leader wants you to evaluate the difference in cycle time between three different offices. Describe the steps you would take in the evaluation in order to provide a report so the leader can take action. In replies to peers, indicate whether you agree or disagree with the steps they outlined. Justify your response using what you learned from the topic materials.

In your own words, describe the difference between Among Group Variation and Within Group Variation. Discuss how you would evaluate the variation and other methods to ensure that the data is appropriate to use for the test. Illustrate using a specific example.

1a. Suppose I have a gaming web site that can only handle 10 players at the same time, or else my server will crash. I have 50 users. Each user is online and playing the game 20% of the time. What is the probability that my server will crash. 1b Now suppose that it is acceptable if the crashing probability is less than 1%. What is the maximum number of users my server can handle? 1c. What is the maximum number of users I can support if my server is twice as large and can handle 20 simultaneous players?

A weekly time ticket for Joyce Caldwell follows:    

Required:
Prepare a journal entry to record Joyce’s wages. (If no entry is required for a transaction/event, select "No Journal Entry Required" in the first account field.)

     

A large school district claims that 80% of the children are from low-income families. 130 children from the district are chosen to participate in a community project. Of the 130 only 72% are from low-income families. The children were supposed to be randomly selected. Do you think they really were?

a. The null hypothesis is that the children were randomly chosen. This translates into drawing times

at random
with replacement
without replacement

from a null box that contains

b.
130 tickets, 72% marked "1" and 28% marked "0"
Thousands of tickets, 80% marked "1" and 20% marked "0"
Thousands of tickets marked either "1" or "0", but the exact percentages of each are unknown and estimated from our sample.
5 tickets, 1 marked "1" and 4 marked "0"

c. What is the expected value of the percent of 1's in the draws? (Don't type in the % sign)

%

d. What is the SD of the null box? (Note: We don't have to estimate the SD of the box from the sample SD because we can compute it directly from the percent of 1's in the null box. This is why we never use a t-test for problems that can be translated into 0-1 boxes.)

e. What is the standard error of the % of 1's in the draws? (Round to 2 decimal places.) %

f. What is the value of the test statistic z? (Round answer to 2 decimal places.)

g. What is the p-value? Click here to view the normal table
%

h. What do you conclude?
There is very strong evidence to reject the null, and conclude that the children were not randomly chosen.
We cannot reject the null, it's plausible the children were randomly chosen.

Danielle and William are visiting an ice cream shop where they will randomly choose one of the following five regular and premium flavors.

Flavors Price

Vanilla Bean $2.00

Chocolate Mint $3.00

Pralines and Cream $4.00

Strawberry Shortcake $5.00

Fudge Brownie Caramel Cheesecake Deluxe $6.00

Define the population as the five services and a sample of size two as the flavor that Danielle chooses and the service that William chooses.

a. Identify the frequency distribution for the population

b. Identify the frequency distribution for all combinations of samples means for Danielle and William choosing a flavor

c. Verify that the population mean and man of all possible sample means are equal

d. Calculate the standard error.

Suppose you know that the amount of time it takes your friend Susan to get from her residence to class averages  50 minutes, with a standard deviation of 55 minutes. What proportion of Susan's trips to class would take more than  50 minutes? . Enter your answers accurate to two decimal places.

What proportion of her class would take more than  50 minutes?

What proportion of Susan's trips to class would take less than 40 minutes?

What proportion of Susan's trips to class would take more than  50 minutes or less than  40 minutes?

2. A new chemotherapy drug is released to treat leukemia and researchers suspect that the drug may have fewer side effects than the most commonly used drug to treat leukemia. The two drugs have equivalent efficacy. In order to determine if a larger study should be conducted to look into the prevalence of side effects for the two drugs, set up a Mann-Whitney U test at the alpha equals .05 level and interpret its results.

                        Number of Reported Side-Effects

Old Drug           0          1          3          3          5

New Drug          0          0          1          2          4

A) We fail to reject H₀, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 16.5 is greater than the critical U value of 2.

B) We fail to reject H₀, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 8.5 is greater than the critical U value of 2.

C) We reject H₀ in favor of H₁, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 16.5 is greater than the critical U value of 2.

D) We reject H₀ in favor of H₁, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 8.5 is greater than the critical U value of 2.

Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

1. Use these data to develop an estimated regression equation that could be used to predict the ridership given the miles of track.
   
   Compute b₀ and b₁ (to 2 decimals).
   b₁
   b₀
   
   Complete the estimated regression equation (to 2 decimals).
   =  +  x
   
2. Compute the following (to 1 decimal):

   SSE
   SST
   SSR
   MSE

   
   
3. What is the coefficient of determination (to 3 decimals)? Note: report r² between 0 and 1.
   
   
   Does the estimated regression equation provide a good fit?
   SelectYes, it even provides an excellent fitYes, it provides a good fitNo, it does not provide a good fitItem 10
   
4. Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
   (  ,  )
   
5. Suppose that Charlotte is considering construction of a light-rail system with 30 miles of track. Develop a 95% prediction interval for the weekday ridership for the Charlotte system (to 1 decimal).
   (  ,  )

The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenueproducing investments together with annual rates of return are as follows:

The credit union will have $2.4 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments.

• Risk-free securities may not exceed 30% of the total funds available for investment.
• Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).
• Furniture loans plus other secured loans may not exceed the automobile loans.
• Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.

How should the $2.4 million be allocated to each of the loan/investment alternatives to maximize total annual return? Round your answers to the nearest dollar.

What is the projected total annual return? Round your answer to the nearest dollar.

$  

A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 24 newly graduated law students. Their scores give a sample standard deviation of 63points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60.

(a) Find a 99% confidence interval for the population variance. (Round your answers to two decimal places.)

(b) Find a 99% confidence interval for the population standard deviation. (Round your answers to two decimal places.)

Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately σ² = 5.1. Suppose a recent study of age at first marriage for a random sample of 31 women in rural Quebec gave a sample variance s² = 2.9. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence interval for the population variance.

(a) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

Do students reduce study time in classes where they achieve a higher midterm score? In a Journal of Economic Education article (Winter 2005), Gregory Krohn and Catherine O’Connor studied student effort and performance in a class over a semester. In an intermediate macroeconomics course, they found that “students respond to higher midterm scores by reducing the number of hours they subsequently allocate to studying for the course.” Suppose that a random sample of n = 8 students who performed well on the midterm exam was taken and weekly study times before and after the exam were compared. The resulting data are given in Table 10.6. Assume that the population of all possible paired differences is normally distributed.

Table 10.6

Paired T-Test and CI: Study Before, Study After

95% CI for mean difference: (3.73660, 12.51340)

T-Test of mean difference = 0 (vs not = 0): T-Value = 4.38, P-Value = .0032

(a) Set up the null and alternative hypotheses to test whether there is a difference in the true mean study time before and after the midterm exam.

H₀: µ_d =  versus H_a: µ_d ?

(b) Above we present the MINITAB output for the paired differences test. Use the output and critical values to test the hypotheses at the .10, .05, and .01 level of significance. Has the true mean study time changed?(Round your answer to 2 decimal places.)

t =   We have (Click to select)strongvery strongextremely strongno evidence.

(c) Use the p-value to test the hypotheses at the .10, .05, and .01 level of significance. How much evidence is there against the null hypothesis?

There is (Click to select)no evidencevery strong evidencestrong evidenceextermly strong evidence against the null hypothesis.

Measurements were recorded for the slapshot speed of 100 minor-league hockey players. These measurements were found to be normally distributed with mean of 84.388 mph and standard deviation of 3.3706 mph. Would it be unusual to record a value above 94.6 mph?

Question 6 options:

According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0499 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 337 independent returns from this year, what is the probability that at least 26 will be fraudulent or will contain errors that are purposely made to cheat the IRS?

Question 7 options:

According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0362 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 385 independent returns from this year, what is the probability that less than 9 will be fraudulent or will contain errors that are purposely made to cheat the IRS?

Question 9 options: