Wildlife biologists inspect 158 deer taken by hunters and find 38 of them carrying ticks that test positive for Lyme disease.

a) Create a 90% confidence interval for the percentage of deer that may carry such ticks.

b) If the scientists want to cut the margin of error in half, how many deer must they inspect?

For a certain wine, the mean pH (a measure of acidity) is supposed to be 3.32 with a known standard deviation of σ = .14. The quality inspector examines 31 bottles at random to test whether the pH is too low, using a left-tailed test at α = 0.05.

(a) What is the power of this test if the true mean is μ = 3.30?

(b) What is the power of this test if the true mean is μ = 3.28?

(c) What is the power of this test if the true mean is μ = 3.26?

A medical researcher is studying the effects of a drug on blood pressure. Subjects in the study have their blood pressure taken at the beginning of the study. After being on the medication for 4 weeks, their blood pressure is taken again. The change in blood pressure is recorded and used in doing the hypothesis test.

Change: Final Blood Pressure - Initial Blood Pressure

The researcher wants to know if there is evidence that the drug increases blood pressure. At the end of 4 weeks, 35 subjects in the study had an average change in blood pressure of 2.1 with a standard deviation of 5.2.

Find the $p$-value for the hypothesis test.

Your answer should be rounded to 4 decimal places.

Ask Your Teacher

The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the weights of these loaves varies. The mean weight is 2 lb. and 3 oz., or 992 grams. Assume the standard deviation of the weights is 30 grams and a sample of 35 loaves is to be randomly selected.

(b) Find the mean of this sampling distribution. (Give your answer correct to nearest whole number.)
grams

(c) Find the standard error of this sampling distribution. (Give your answer correct to two decimal places.)


(d) What is the probability that this sample mean will be between 988 and 996? (Give your answer correct to four decimal places.)


(e) What is the probability that the sample mean will have a value less than 986? (Give your answer correct to four decimal places.)


(f) What is the probability that the sample mean will be within 2 grams of the mean? (Give your answer correct to four decimal places.)

1. How did you construct the confidence interval (put the formula into words) and Please mention how to find your critical values

2. . And then I need two comparisons/contrasts: compare the 90% and 95% confidence intervals within a group, is one longer than the other? If so, why?

3. Finally, compare the 95% confidence intervals across groups. Is there any overlap in the intervals or is one interval completely greater than the other?

mean: 24025.4 (NY) and 12247.21 (TX)

std. deviation: 16049.05(NY) and 9448.70(TX) respectively

And sample size n=50 for both

Given a recent outbreak of illness caused by E. coli bacteria, the mayor in a large city is concerned that some of his restaurant inspectors are not consistent with their evaluations of a restaurant’s cleanliness. In order to investigate this possibility, the mayor has five restaurant inspectors grade (scale of 0 to 100) the cleanliness of three restaurants. The results are shown in the accompanying table. (You may find it useful to reference the q table.)

An ordinary deck of playing cards has 52 cards. There are four suits-​spades, ​hearts, diamonds, and clubs with 13 cards in each suit. Spades and clubs are​ black; hearts and diamonds are red. If one of these cards is selected at​ random, what is the probability for a nine, black, not a heart

The probability of selecting a nine is:
The probability of selecting a black card is:
The probability of selecting a card that is not heart is:
(type an integer or a simplified fraction for all answers)

A company has developed a design for a high-quality portable printer. The two key components of manufacturing cost are direct labor and parts. During a testing period, the company has developed prototypes and conducted extensive product tests with the new printer. The company's engineers have developed the bivariate probability distribution shown below for the manufacturing costs. Parts cost (in dollars) per printer is represented by the random variable x and direct labor cost (in dollars) per printer is represented by the random variable y. Management would like to use this probability distribution to estimate manufacturing costs.

(a)

Show the marginal distribution of direct labor cost and compute its expected value (in dollars), variance, and standard deviation (in dollars). (Round your answer for standard deviation to the nearest cent.)

(b)

Show the marginal distribution of parts cost and compute its expected value (in dollars), variance, and standard deviation (in dollars). (Round your answer for standard deviation to the nearest cent.)

(c)

Total manufacturing cost per unit is the sum of direct labor cost and parts cost. Show the probability distribution for total manufacturing cost per unit.

(d)

Compute the expected value (in dollars), variance, and standard deviation (in dollars) of total manufacturing cost per unit. (Round your answer for standard deviation to two decimal places.)

expected value dollarsvariancestandard deviation dollars

(e)

Are direct labor and parts costs independent? Why or why not?

Since the covariance equals  , which  ---Select--- is is not equal to zero, we can conclude that direct labor cost  ---Select--- is is not independent of parts cost.

If you conclude that direct labor and parts costs are not independent, what is the relationship between direct labor and parts cost?

There is a positive correlation between the costs of direct labor and parts.There is a negative correlation between the costs of direct labor and parts.    The costs of direct labor and parts are independent.

(f)

The company produced 1,700 printers for its product introduction. The total manufacturing cost was $198,450. Is that about what you would expect?

The expected manufacturing cost for 1,700 printers is $  which is  ---Select--- lower than higher than equal to $198,450.

If it is higher or lower, what do you think may have caused it? (Select all that apply.)

A supplier increased the cost of one of the more common printer parts this company uses in the manufacturing process.At first there was a steep learning curve, but as more printers were manufactured direct labor costs decreased.There was an increase in the cost of direct labor due to an influx of many new employees.The expected manufacturing cost is equal to $198,450.

Assume that random variable x^2 has a chi-squared distribution with v degree of freedom. Find the value of “A” for the following cases

1) P(X^2 <=A) =.95 when v = 6

2) P(X^2>=A) =.01 when v = 21

3) P(A <= X^2 <= 23.21)= .015 when v = 10.

A recent survey of math students asked about their overall grades. 22 students were surveyed, and it was found that the average GPA of the 22 sampled students was a 3.2, with a standard deviation of 0.9 points. Calculate a 90% confidence interval for the true mean GPA of math students. Round your answer to the nearest hundredth, and choose the most correct option below: (2.88,3.52), (2.87,3.53), (.28,.94), (2.40,4.00) or none of the above...

The grade point average for 7 randomly selected college students is:
2.3, 2.6, 1.2, 3.5, 2.3, 3.1, 1.3.( Assume the sample is taken from a normal distribution)
a) Find the sample mean. (show all work)
b) Find the sample standard deviation.
c) Construct a 90% C. I. for the population mean

To create the following problem the other problem with all samples n =5; the same sample means and variances that appeared in the problem were used but the sample size was doubled to n = 10.

a. Predict how the increase in sample size should affect the F-ratio for these data compared to the values obtained in the other problem (F= 3.50). Use an ANOVA with a = 0.05 to check your prediction. Note: Because the samples are all the same size MS_within is the average of the three sample variances.

b. Predict how the increase in sample size should affect the value of η² for these data compared to the  η² in the other problem ( η² = 0.368)

Q1) A group of wine enthusiasts tested a pinot noir wine from Oregon. The evaluation was to grade the wine on a 0 to 100 point scale. The results are as follows: 92 86 92 91 91 86 89 91 91 90 90 93 87 90 91 92 89 86 89 90 88 83 91 88 89 92 87 89 85 92 85 91 84 89 88 82 85 90 90 82 a) (5 points) Display descriptive statistics for the given data by using MINITAB. b) (5 points) Prepare a box plot of the given data by using MINITAB. c) (5 points) Mark the mean, median and outliers on the graph. d) (5 points) Based on the box plot, comment on the shape of the distribution.

Part 2– R work (must be done in R)

Copy and paste your R code and output into a word document, along with your written answers to the questions, and upload to Canvas.  

Follow these instructions to import the necessary dataset:

Before opening the dataset needed for this problem, you’ll need to call the “car”package.  Run the following line of code:

> library(car)

Now you can import the “Prestige” dataset and use it to answer the question below. Name the data frame with your UT EID:

> my_eid <- Prestige

Remember to include any code you use along with your answers in your submission!

ThePrestigedataset contains information about different occupations in Canada in 1971.  We want to see if the average years of education of the workforce (“education”) can predict an occupation’s annual income (“income”).

Make a scatterplot for this analysis.  Why is a linear regression not appropriate? (1pt)

Create a new variable in the dataset called “log_income” that is the natural log of each income value. (1pt)

Conduct a full analysis to see if education can predict log-income.  Include all steps for full credit.  Comment on any assumptions that might not be met, but carry out the full test.   (4pt)

1. An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.2 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 150 engines and the mean pressure was 4.3 pounds/square inch. Assume the standard deviation is known to be 0.8. A level of significance of 0.05 will be used. Determine the decision rule.

Enter the decision rule.

2. A lumber company is making doors that are 2058.0 millimeters tall. If the doors are too long they must be trimmed, and if the doors are too short they cannot be used. A sample of 20 is made, and it is found that they have a mean of 2047.0 millimeters with a standard deviation of 30.0. A level of significance of 0.1 will be used to determine if the doors are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.

3. An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 7.9 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 8.1 pounds/square inch with a variance of 0.25. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.

4. A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 413.0 gram setting. It is believed that the machine is underfilling the bags. A 33 bag sample had a mean of 406.0 grams. A level of significance of 0.02 will be used. Is there sufficient evidence to support the claim that the bags are underfilled? Assume the variance is known to be 256.00.

What is the conclusion?

A. There is not sufficient evidence to support the claim that the bags are undefilled.

B. There is sufficient evidence to support the claim that the bags are underfilled.

5.

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 404.0 gram setting. It is believed that the machine is underfilling the bags. A 39 bag sample had a mean of 400.0 grams. A level of significance of 0.05 will be used. Is there sufficient evidence to support the claim that the bags are underfilled? Assume the standard deviation is known to be 26.0.

What is the conclusion?

A. There is not sufficient evidence to support the claim that the bags are undefilled.

B. There is sufficient evidence to support the claim that the bags are underfilled.