What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.92 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.43 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)

5.30 A concern to public health officials is whether a concentration of lead in the paint of older
homes may have an effect on the muscular development of young children. In order to evaluate
this phenomenon, a researcher exposed 90 newly born mice to paint containing a specified
amount of lead. The number of Type 2 fibers in the skeletal muscle was determined 6 weeks
after exposure. The mean number of Type 2 fibers in the skeletal muscles of normal mice of this
age is 21.7. The n=90 mice yielded y(mean)=8.8, s=15.3. Is there significant evidence in the data
to support the hypothesis that the mean number of Type 2 fibers is different from 21.7 using an
alpha = .05 test?

Question: How to run in R?

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.† Over a period of months, an adult male patient has taken thirteen blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.81 mg/dl.

(a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

n is largeuniform distribution of uric acidσ is unknownnormal distribution of uric acidσ is known

(c) Interpret your results in the context of this problem.

There is a 5% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.The probability that this interval contains the true average uric acid level for this patient is 0.95.    There is not enough information to make an interpretation.The probability that this interval contains the true average uric acid level for this patient is 0.05.There is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient.

(d) Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.02 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)
blood tests

What is the value of research in your everyday life and when you are completing a graduate degree?

1. The thickness of a printed circuit board is an important quality parameter. Data on board thickness (in inches) are given in Table 6 for 25 samples of three boards each.
   (a) Set up x-bar and R control charts. Is the process in statistical control?
   (b) Estimate the process standard deviation.
   (c) What are the limits that you would expect to contain nearly all the process measurements?
   (d) If the specifications are at 0.0630 in. ± 0.0015 in.,
   what is the value of the PCR Cp?     

                                Table 6

   Sample No.       X1                  X2              X3

   1                         0.0629       0.0636       0.0640

   2                         0.0630       0.0631      0.0622

   3                        0.0628        0.0631    0.0633

   4                        0.0634        0.0630      0.0631

   5                        0.0619       0.0628       0.0630

   6                       0.0613       0.0629      0.0634

   7                        0.0630       0.0639      0.0625

   8                        0.0628       0.0627      0.0623                  

   9                         0.0623      0.0627      0.0633

   10                       0.0631      0.0631     0.0633

   11                      0.0635      0.0630     0.0638

   12                       0.0623      0.0630     0.0630

   13                      0.0635      0.0631     0.0630

   14                       0.0645      0.0640     0.0631

   15                       0.0619      0.0644     0.0632

   16                      0.0631     0.0627      0.0630

   17                      0.0616       0.0623     0.0631

   18                      0.0630       0.0630     0.0626

   19                      0.0636       0.0631     0.0629

   20                      0.0640       0.0635    0.0629

   21                      0.0628       0.0625     0.0616

   22                      0.0615       0.0625     0.0619

   23                      0.0630       0.0632     0.0630

   24                      0.0635       0.0629    0.0635

   25                       0.0623      0.0629    0.0630

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6150 and estimated standard deviation σ = 2750. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)


(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?

The probability distribution of x is approximately normal with μ_x = 6150 and σ_x = 2750.The probability distribution of x is approximately normal with μ_x = 6150 and σ_x = 1944.54.    The probability distribution of x is approximately normal with μ_x = 6150 and σ_x = 1375.00.The probability distribution of x is not normal.

What is the probability of x < 3500? (Round your answer to four decimal places.)


(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)


(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?

The probabilities increased as n increased.The probabilities decreased as n increased.    The probabilities stayed the same as n increased.

If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.    It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

Two critics rate the service at six award-winning restaurants on a continuous 0 to 10 scale. Their rankings are shown in the table below. Restaurant 1 2 3 4 5 6 Critic 1: 6.1 5.2 8.9 7.4 4.3 9.7 Critic 2: 7.3 5.5 9.1 7.0 5.1 9.8

a) Is this paired or unpaired data?

b) Compute a 95% confidence interval for the mean difference in rating. Show all your working.

c) Is there a difference between the critics’ ratings, allowing for some random variation? Answer this question using a parametric hypothesis test, and compare your result to the confidence interval from part b.

d) Use a nonparametric hypothesis test to further investigate whether there is a difference between the critics’ rankings.

e) Is the parametric or non-parametric test more appropriate here?

A worker has asked her supervisor for a confidential letter of recommendation for a new job. She estimates that there is an 80% chance that she will get the job if she receives a strong recommendation, a 40% chance if she receives a moderately good recommendation, and a 10% if she receives a weak recommendation. She further estimates that the probabilities that the recommendation will be strong, moderate and weak are 0.6, 0.3 and 0.1 respectively. Given that she fails to get the job, what is the probability that she received a weak recommendation?

1. Assume that the mean adjusted hippocampal volume for healthy adolescents is 9.01 cubic centimeters. State the hypotheses to test whether the AOAUD mean hippocampal volume is less than this value.

To perform the hypothesis test, we will compute H₀: m = 9.01 and H_A: m < 9.01. By doing this, we get the results:

Hypothesis test results:

2. Compute the t-value and the P-value for this test.

?

Consider four nonstandard dice, whose sides are labeled as follows (the 6 sides on each die are equally likely).

A: 4, 4, 4, 4, 0, 0

B: 3, 3, 3, 3, 3, 3

C: 6, 6, 2, 2, 2, 2

D: 5, 5, 5, 1, 1, 1

These four dice are each rolled once. Let A be the result for die A, B be the result for die B, etc.

(a) Find P(A > B), P(B > C), P(C >D), and P(D > A).

(b) Is the event A > B independent of the event B > C? Is the event B > C independent of the event C >D? Explain.

discuss the interface of mathematics/statistics, computer science and other disciplines focusing on people, events and ideas

To investigate an alleged unfair trade practice, the Federal Trade Commission (FTC) takes a random sample of sixteen “5- ounce” candy bars from a large shipment. The mean of the sample weights is 4.85 ounces and the sample standard deviation is 0.1 ounce. It is reasonable to assume the population of candy bar weights is approximately Normally distributed. Based on this sample, does the FTC have grounds to proceed against the manufacturer for the unfair practice of short-weight selling, on average? Answer this question by completing the following steps of a hypothesis test at the 5% significance level.

d. Do you reject or fail to reject the null hypothesis? Why?

e. Does the FTC have grounds to proceed against the manufacturer for the unfair practice of short-weight selling, on average? Explain your answer.

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(a)

• Suppose n = 45 and
• p = 0.13.

(For each answer, enter a number. Use 2 decimal places.)
n·p =  
n·q =  

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo     

second blank

cancannot     

third blank

both n·p and n·q exceedn·p and n·q do not exceed     n·q exceedsn·q does not exceedn·p exceedsn·p does not exceed

fourth blank (Enter an exact number.)


What are the values of μ_p̂ and σ_p̂? (For each answer, enter a number. Use 3 decimal places.)
μ_p̂ = mu sub p hat =

σ_p̂ = sigma sub p hat =

(b)

Suppose

• n = 25 and
• p = 0.15.

Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo     

second blank

cancannot     

third blank

both n·p and n·q exceedn·p and n·q do not exceed     n·q exceedsn·q does not exceedn·p exceedsn·p does not exceed

fourth blank (Enter an exact number.)

(c)

Suppose

• n = 59 and
• p = 0.40.

(For each answer, enter a number. Use 2 decimal places.)
n·p =  
n·q =  

Can we approximate  p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo     

second blank

cancannot     

third blank

both n·p and n·q exceedn·p and n·q do not exceed     n·q exceedsn·q does not exceedn·p exceedsn·p does not exceed

fourth blank (Enter an exact number.)


What are the values of μ_p̂ and σ_p̂? (For each answer, enter a number. Use 3 decimal places.)
μ_p̂ = mu sub p hat =

σ_p̂ = sigma sub p hat =

All work must be done in R programing. Consider this dataset provided to you as prob10.txt c1 t1 c2 t2 c3 t3 c4 t4 2650 3115 2619 2933 2331 2799 2750 3200 1200 1101 1200 1309 1888 1901 1315 980 1541 1358 1401 1499 1256 1238 1625 1421 1545 1910 1652 2028 1449 1901 1399 2002 1956 2999 2066 2880 1777 2898 1999 2798 1599 2710 1754 2765 1434 2689 1702 2402 2430 2589 2789 2899 2332 2300 2250 2741 1902 1910 2028 2100 1888 1901 2000 1899 1530 2329 1660 2332 1501 2298 1478 2287 2008 2485 2104 2871 1987 2650 2100 2520 (2) Read it in and set the row names to “Gene 1” through “Gene 10” It should look like this in R > prob10 c1 t1 c2 t2 c3 t3 c4 t4 Gene 1 2650 3115 2619 2933 2331 2799 2750 3200 Gene 2 1200 1101 1200 1309 1888 1901 1315 980 Gene 3 1541 1358 1401 1499 1256 1238 1625 1421 Gene 4 1545 1910 1652 2028 1449 1901 1399 2002 Gene 5 1956 2999 2066 2880 1777 2898 1999 2798 Gene 6 1599 2710 1754 2765 1434 2689 1702 2402 Gene 7 2430 2589 2789 2899 2332 2300 2250 2741 Gene 8 1902 1910 2028 2100 1888 1901 2000 1899 Gene 9 1530 2329 1660 2332 1501 2298 1478 2287 Gene 10 2008 2485 2104 2871 1987 2650 2100 2520 (3 )Perform a one-sample t-test to compare the hypothesis that the mean of the control expression values is 2000.

Determine the margin of error for a confidence interval to estimate the population mean with n=18 and s=12.1 for the confidence levels below.

A) The margin of error for an 80% confidence interval is:

B) The margin of error for an 90% confidence interval is:

C) The margin of error for an 99% confidence interval is: