The table below shows the number of students absent on the particular day of the week:

Test if the distribution of students absent is uniform through the week with the significance level of 5%.

During the COVID-19 pandemic, the hospital emergency department at a very busy hospital receives, on average, one patient every 25.1 minutes. The standard deviation of inter-arrival time between two consecutive patients is 9.8 minutes. Calculate the average patients arrival (receiving) rate per day for this hospital emergency service. Note that, the emergency service of this hospital is open 24/7, and one day is equivalent to 24 hours.

1. A state’s Division of Motor Vehicles (DMV) claims that 60% of all teens pass their driving test on the
first attempt. An investigative reporter examines an SRS of the DMV records for 125 teens; 56 of them
passed the test on their first try. Is there convincing evidence at the α=0.01 significance level that the
DMV’s claim is lower?

2. In a recent year, 65% of first-year college students responding to a national survey identified “being
very well-off financially” as an important personal goal. A state university finds that 102 of an SRS of
200 of its first-year students say that this goal is important. Is there convincing evidence at
the α=0.05 significance level that the proportion of all first-year students at this university who think
being very well-off is important differs from the national value of 65%?

3. Every road has one at some point—construction zones that have much lower speed limits. To see if
drivers obey these lower speed limits, a police officer uses a radar gun to measure the speed (in miles
per hour, or mph) of a random sample of 10 drivers in a 25 mph construction zone. Here are the data:
27 33 32 21 30 30 29 25 27 34
Is there convincing evidence at the α=0.01 significance level that the average speed of drivers in this
construction zone is greater than the posted speed limit?

4. A school librarian purchases a novel for her library. The publisher claims that the book is written at a fifth-grade reading level, but the librarian suspects that the reading level is lower than that. The librarian selects a random sample of 45 pages and uses a standard readability test to assess the reading level of each page. The mean reading level of these pages is 4.8 with a standard deviation of 0.6. Do these data give convincing evidence at the α=0.01 significance level that the average reading level of this novel is less than 5?

The following table shows the number of full-time faculty that WVU has on staff throughout the years.

(A) Find the equation of the regression line that represents the number of full-time faculty, F , as a function of x years since 2000. (round the regression coefficients to two decimal places)
F(x) =


(B) What is the correlation coefficient (r-value) for the regression model? (Round your answer to three decimal places)
r =

(C) Given the value of r , does the regression line model the data well? That is, does the equation do a good job of modeling the data?

Yes, the r-value is low, meaning the data can be modeled using a line

No, the r-value is high, meaning the data can't be modeled using a line    

Yes, the r-value is high, meaning the data can be modeled using a line

No, the r-value is low, meaning the data can't be modeled using a line

(D) Using the regression line, How many Faculty members did WVU have in 2010? (Round your answer to the nearest whole number)

1. Given the following pmf f(x,y), calculate m_x, m_y, s_x, s_y, s_xy, p_xy, and E[2.5x²-10y³-8x³y²+3]

x2 is the same as x^2, and x3 is  x^3,y2 is y^2

Suppose we take a poll (random sample) of 3907 students classified as Juniors and find that 2904 of them believe that they will find a job immediately after graduation.

What is the 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation.

1. (0.725, 0.761)
2. (0.732, 0.755)
3. (0.73, 0.757)
4. (0.736, 0.75)

When survey data indicated that a company needed to improve its​ package-sealing process, an experiment was conducted to determine the factors in the​ bag-sealing equipment that might be affecting the ease of opening the bags without tearing the inner liner of the bag. Data were collected on 19 bags and the plate gap on the​ bag-sealing equipment was used to predict the tear rating of a bag. The results are displayed in the accompanying table and the regression equation is the following. Complete parts​ (a) through​ (c).

ModifyingAbove Upper Y with caret Subscript iYiequals=0.79060.7906plus+0.46820.4682Xi​,

with

Summation from i equals 1 to n∑i=1nYiequals=14.7414.74​,

Summation from i equals 1 to n∑i=1nUpper Y Subscript i Superscript 2Y2iequals=40.320240.3202​,

and

Summation from i equals 1 to n∑i=1nXiYiequals=20.1720.17.

a. Determine the coefficient of​ determination, r2​,and interpret its meaning.

What is the meaning of the coefficient of​determination? (Choose Below)

A. It measures the variability in the actual plate gap from the predicted plate gap.

B. It measures the variability in the actual tear rating from the predicted tear rating.

C. It is the proportion of the variation in the plate gap that is explained by the variability in the tear rating.

D. It is the proportion of the variation in the tear rating that is explained by the variability in the plate gap.

b. Determine the standard error of the estimate.

SYX = ___? ​(Round to four decimal places as​needed.)

c. How useful do you think this regression model is for predicting the tear rating based on the plate gap in the​bag-sealing equipment? (Choose Below)

What is the meaning of the coefficient of​determination? (Choose Below)

A. It measures the variability in the actual plate gap from the predicted plate gap.

B. It measures the variability in the actual tear rating from the predicted tear rating.

C. It is the proportion of the variation in the plate gap that is explained by the variability in the tear rating.

D. It is the proportion of the variation in the tear rating that is explained by the variability in the plate gap.

b. Determine the standard error of the estimate.

SYX = ___? ​(Round to four decimal places as​needed.)

c. How useful do you think this regression model is for predicting the tear rating based on the plate gap in the​bag-sealing equipment? (Choose Below)

The following are the grades of 27 students in a statistics exam: 20 28 42 51 54 55 56 57 9 61 62 63 64 65 67 68 69 71 74 75 76 77 79 81 84 86 100 a. The number of classes is 5, construct a frequency table. b. Draw a histogram. c. Construct stem and leaf diagram

SHOW WORK!!!!! Full credit will not be given for answers only. NOTE: for any question asking you to determine a probability----you MUST write out a probability statement using proper notation!!!! Probabilities should be DECIMAL form and rounded to 4 decimal places.

A company manufactures windows that are inserted into automobiles. Each window has five studs for attaching it. A pullout test is used to determine the force required to pull a stud out of a window (i.e. Destructive testing). Let F be the force required for pulling studs out of position. Thirty observations of F were as follows:

159 156 165 142 160 167
151 160 158 148 165 137
161 147 167 158 151 155
120 140 149 160 157 150
137 138 155 144 147 164

NOTE: you can copy and paste the data set into Excel to make it easier to work with. It is acceptable to use excel and summarize the equations/steps used on your homework paper.

a) Create a stem-and-leaf plot.
b) Calculate the sample mean and sample variance.
c) Determine the 5-number summary.
d) Do any outliers exist in our data? If so, identify them and mathematically justify your answer.
e) Construct a well-labeled modified boxplot.
f) Find the 78th percentile.
g) Does the data set appear to be skewed or symmetric? If it is skewed, decide in what direction. Explain your answer.

[20 pts] In a random poll taken in 2008, Gallup asked 1010 national adults whether they were baseball fans. 570 of the sample said they were. Construct a 96% confidence interval to estimate the proportion of national adults who are baseball fans. Use 4 non-zero decimal places in your calculations.

a)Za/2

b)Find σp̂

c)Find the margin of error and construct the confidence interval

. Consider the 68 words in the following two sentences to be modeled as random variables. The sentences contain words of 1 letter length to 10 letter length. Thus random variable x lies in the range 1 ≤ x ≤ 11

        “A single link flexible arm is a dynamic system with the first eigenvalue equal to zero and giving the primary rigid body motion and the eigenvalues greater than zero giving flexural vibration that may occur during the response. The object is to drive the arm tip to a constant steady state position in as fast a time as possible while keeping the arm tip vibration to a minimum.”

(A) Develop a bar graph for the number of words with a specific number of letters.

For example, in the phrase “This is an example for the type of words related to this problem”:   3 two letter words, 2 three letter words, 3 four letter words, 1 five letter word, 3 seven letter words.

(B) Calculate the probability density distribution and show it bar form. Use 1 for the transition from probability to probability density which makes these two the same.

(C)    Determine the mean μ and standard deviation σ.

(D)   Use part B result and determine the probability that a word falls between

            μ-σ and μ+σ.

   (E) If the system is modeled with a continuous normal probability distribution, determine the probability that a word falls between 6 and 9 letters.

Kellie a developmental psychologist measured the number of errors twenty teenagers made in a driving simulator while talking on their cellphones.

Here are the data [1, 2, 5, 2, 1, 3, 1, 4, 1, 2, 1, 25, 1, 4, 1, 40, 1, 2, 1, 1]

6) Calculate the mean, median and mode for this set of data.

7) Which measure of central tendency most accurately describes Kellie’s data? Briefly explain why.  

The following lists two variables taken from a survey of recent college graduates: Cumulative First year’s salary College GPA (in 1,000’s) Joe 3.1 28 Suzy 2.5 22 Catherine 3.6 29 Simon 2.8 25 Jethro 2.7 27 Shannon 3.3 30 Vonda 3.4 32 Zane 3.5 28 Use the data to answer the following: a. Draw a scatter diagram depicting the relationship between these two variables. Interpret. b. Calculate the coefficient of correlation. Interpret. c. Calculate the coefficient of determination. Interpret. d. Develop a regression equation for this data e. Using your regression equation, what would you predict Geraldine's first year salary to be if she graduated with a 3.15 G.P.A.?

The Thomas Supply Company Inc. is a distributor of gas-powered generators. As with any business, the length of time customers take to pay their invoices is important. Listed below, arranged from smallest to largest, is the time, in days, for a sample of the Thomas Supply Company Inc. invoices.

Click here for the Excel Data File
(Round your answers to 2 decimal places.)

1. Determine the first and third quartiles.
2. Determine the second decile and the eighth decile.
3. Determine the 67^th percentile.

1.

perform Levene’s test for equal variance. Note, this is a one‐way ANOVA testing for the equality of 16 variances (each combination of promotion/discount). 0.1 signigicance

2. perform 2-way anova with replication

To answer these questions, an experiment was designed using laundry detergent pods. For ten weeks, 160 subjects received information about the products. The factors under consideration were the number of promotions (1, 3, 5, or 7) that were described during this ten‐ week period and the percent that the product was discounted (10%, 20%, 30%, or 40%) off the average non‐promotional price. Ten individuals were randomly assigned to each of the sixteen combinations. The data reflecting what the sub‐ jects would expect to pay for the product (i.e., their reference price) at the end of the 10‐week period. 0.1 significance