A political polling company wants to know if there are differences among people of different political parties with respect to their views on a bill recently proposed in Congress. The company conducted a survey of 300 people and got the following results. Do the results support the hypothesis that there are differences among people in different political parties regarding their views on this bill? (Use a = 0.10)

Your instructor randomly chose a coin with probability 0.5 and asks you to decide which coin he chose according to the outcome of 3 tosses: Tossing coin 1 yields a head with a probability P(X1 = H) = .3 (and tail with P(X1 = T) = .7). Tossing coin 2 yields a head with a probability P(X2 = H) = .6 (and tail with P(X2 = T) = .4). You earn $1 if you correctly guessed the coin and $0 otherwise. Design the optimum decision rule and estimate your average earning. (Using the Bayesian Theory concept)

using excel and it's functions

The table shows a sample of the maximum capacity (maximum number of spectators) of sports stadiums. The table does not include horse-racing or motor-racing stadiums.

a) Calculate the sample mean and the sample standard deviation for the maximum capacity of sports stadiums (the data).

b) Let the sample mean approximate μ and the sample standard deviation approximate σ. The distribution of X can then be approximated by X ~ _____(_____,_____).

c) Use the distribution in part e to calculate the probability that the maximum capacity of sports stadiums is less than 67,000 spectators.

d) Determine the cumulative relative frequency that the maximum capacity of sports stadiums is less than 67,000 spectators. Hint: Order the data and count the sports stadiums that have a maximum capacity less than 67,000. Divide by the total number of sports stadiums in the sample.

e) Why aren’t the answers to part f and part g exactly the same?

Organic chemists often purify organic compounds by a method known as fractional crystallization. An experimenter wanted to prepare and purify 4.85 g of aniline. Ten 4.85 g quantities of aniline were individually prepared and purified to acetanilide. The following dry yields were recorded. 3.83 3.81 3.89 3.87 3.90 3.37 3.63 4.01 3.70 3.82

Estimate the mean grams of acetanilide that can be recovered from an initial amount of 4.85 g of aniline. Use a 95% confidence interval. (Round your answers to three decimal places.)

A hospital human resource manager wants to investigate the relationship between burnout and nurses being absent from work. The manager collects absence and "psychological burnout" from a random sample of nurses at the hospital. What can the manger conclude with an α of 0.10?

a) What is the appropriate statistic?
---Select one--- (na, Correlation, Slope, Chi-Square)
Compute the statistic selected in a):  

b) Input the appropriate value(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =  ; Decision:  ---Select one--- (Reject H0, Fail to reject H0)

c) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
effect size =  ;    ---Select one--- (na, trivial effect, small effect, medium effect, large effect)

d) Make an interpretation based on the results.

a. There is a significant positive relationship between being absent from work and burnout.

b. There is a significant negative relationship between being absent from work and burnout.

c. There is no significant relationship between being absent from work and burnout.

*****Please answer ALL questions*****

Question 6 (1 point)

A statistics professor wants to examine the number of hours that seniors and freshmen study for the final. Specifically, the professor wants to test if the average number of hours that seniors study is greater than the average number of hours that freshmen study. If the seniors are considered group 1 and the freshmen are considered group 2, what are the hypotheses for this scenario?

Question 6 options:

Question 7 (1 point)

A pharmaceutical company is testing a new drug to increase memorization ability. It takes a sample of individuals and splits them randomly into two groups: group 1 takes the drug, group 2 takes a placebo. After the drug regimen is completed, all members of the study are given a test for memorization ability with higher scores representing a better ability to memorize. Those 21 participants on the drug had an average test score of 21.85 (SD = 4.22) while those 28 participants not on the drug (taking the placebo) had an average score of 20.94 (SD = 6.504). You use this information to perform a test for two independent samples with hypotheses Null Hypothesis: μ₁ = μ₂, Alternative Hypothesis: μ₁ ≠ μ₂. What is the test statistic and p-value? Assume the population standard deviations are equal.

Question 7 options:

Question 8 (1 point)

You are interested in whether the average lifetime of Duracell AAA batteries is greater than the average lifetime of Energizer AAA batteries. You lay out your hypotheses as follows: Null Hypothesis: μ₁ ≤ μ₂, Alternative Hypothesis: μ₁ > μ₂. After running a two independent samples t-test, you see a p-value of 0.6598. What is the appropriate conclusion?

Question 8 options:

Question 9 (1 point)

It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before. Suppose you want to test the hypothesis that students who study one week before score less than students who study the night before. A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.0362. What is the appropriate conclusion?

Question 9 options:

Question 10 (1 point)

A medical researcher wants to examine the relationship of the blood pressure of patients before and after a procedure. She takes a sample of people and measures their blood pressure before undergoing the procedure. Afterwards, she takes the same sample of people and measures their blood pressure again. If the researcher wants to test if the blood pressure measurements after the procedure are less than the blood pressure measurements before the procedure, what will the null and alternative hypotheses be? Treat the differences as (blood pressure after - blood pressure before).

Question 10 options:

*****Please answer all questions*****

Question 1 (1 point)

Consumers Energy states that the average electric bill across the state is $39.09. You want to test the claim that the average bill amount is actually different from $39.09. What are the appropriate hypotheses for this test?

Question 1 options:

Question 2 (1 point)

A medical researcher wants to determine if the average hospital stay after a certain procedure is greater than 12.41 days. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≤ 12.41, Alternative Hypothesis: μ > 12.41. If the researcher randomly samples 22 patients that underwent the procedure and determines their average hospital stay was 14.93 days with a standard deviation of 6.108 days, what is the test statistic and p-value of this test?

Question 2 options:

Question 3 (1 point)

Suppose the national average dollar amount for an automobile insurance claim is $566.2. You work for an agency in Michigan and you are interested in whether or not the state average is different from the national average. The hypotheses for this scenario are as follows: Null Hypothesis: μ = 566.2, Alternative Hypothesis: μ ≠ 566.2. A random sample of 89 claims shows an average amount of $574.113 with a standard deviation of $83.7792. What is the test statistic and p-value for this test?

Question 3 options:

Question 4 (1 point)

It is reported in USA Today that the average flight cost nationwide is $414.79. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually less than $414.79. The hypotheses for this situation are as follows: Null Hypothesis: μ ≥ 414.79, Alternative Hypothesis: μ < 414.79. You take a random sample of national flight cost information and perform a one sample mean hypothesis test. You observe a p-value of 0.342. What is the appropriate conclusion? Conclude at the 5% level of significance.

Question 4 options:

Question 5 (1 point)

Consumers Energy states that the average electric bill across the state is $124.59. You want to test the claim that the average bill amount is actually greater than $124.59. The hypotheses for this situation are as follows: Null Hypothesis: μ ≤ 124.59, Alternative Hypothesis: μ > 124.59. You complete a randomized survey throughout the state and perform a one-sample hypothesis test for the mean, which results in a p-value of 0.0187. What is the appropriate conclusion? Conclude at the 5% level of significance.

Question 5 options:

The following table compares the completion percentage and interception percentage of 55 NFL quarterbacks.

Step 4 of 5 :  

Construct the 98% confidence interval for the slope. Round your answers to three decimal places.

Step 5 of 5 :  

Construct the 95% confidence interval for the slope. Round your answers to three decimal places.

Quantitative variable

USD-Food

7040

7089

7051

7000

7179

7036

6971

6943

6937

6953

7073

7097

6991

7130

6935

11795

8925

10363

8634

9294

8455

8633

9157

9397

9101

9231

8902

10740

9321

11077

1. Select one of your quantitative variables.
2. Choose a confidence level (1 – α).
3. Make a confidence interval for your selected variable. Be sure you show all the steps you took. Include a screen shot of any applet you used in your calculations
4. Explain your results in everyday language.

(1 point) Samples were collected from two ponds in the Bahamas to compare salinity values (in parts per thousand). Several samples were drawn at each site.

Pond 1: 37.02, 36.72, 37.03, 38.85, 36.75, 37.54, 37.32

Pond 2: 38.71, 38.53, 39.21, 39.05, 38.89
Use a 0.050.05 significance level to test the claim that the two ponds have the same mean salinity value.

(a) The test statistic is  .

(b) The conclusion is

A. There is not sufficient evidence to indicate that the two ponds have different salinity values.
B. There is sufficient evidence to indicate that the two ponds have different salinity values.

(c) We should

A. not take the results too seriously since neither sample is big enough to be meaningful.
B. remove the largest and smallest values from the larger data set and only test equal size samples.
C. check to see if the data appear close to Normal since the sum of the sample sizes is less than 15.
D. All of the above.

13. Recall the following situation, from a previous exercise: An assembly line worker’s job is to install a particular part in a device, a task which they can do with a probability of success of 0.78 on each attempt. (Assume that a success on one attempt is independent of success on all other previous or future attempts.) Suppose that they need to install ten such parts a day.

(a) What is the probability that it will take them 12 or more tries to install ten such parts? What you provide should be a slight modification of what you provide.

(b) What is the probability that, during a five day work week, it will take the worker 12 or more tries to install all the parts on exactly three of the days?You will need to use your result from part (a), along with a different distribution.

(c) What is the probability that, during a five day work week, it will take the worker less than 12 tries to install all the parts on one or two of the days?

Suppose that the weight of an newborn fawn is Uniformly distributed between 2.2 and 3.1 kg. Suppose that a newborn fawn is randomly selected. Round answers to 4 decimal places when possible.

a. The mean of this distribution is

b. The standard deviation is  

c. The probability that fawn will weigh exactly 2.3 kg is P(x = 2.3) =

d. The probability that a newborn fawn will be weigh between 2.3 and 2.8 is P(2.3 < x < 2.8) =

e. The probability that a newborn fawn will be weigh more than 2.58 is P(x > 2.58) =

f. P(x > 2.3 | x < 2.7) =  

g. Find the 80th percentile.

Statistics Out- of- Control Signals

Out-of-control signal I: Any point falls beyond the ±3σ level.

Out-of-control signal II: A run of nine consecutive points on the same side of the center line.

Out-of-control signal III: At least two of three consecutive points lie beyond the ±2σ level on the same side of the center line.

Yellowstone Park Medical Services provides emergency health care for park visitors. Such health care includes treatment for everything from indigestion and sunburn to more serious injuries. A recent issue of Yellowstone Today indicated that the average number of visitors treated each day was 21.7. The estimated standard deviation was 4.2.

For a ten- day summer period, the following data were obtained:

Day 1 2 3 4 5 6 7 8 9 10

Number Treated 20 15 12 21 24 28 32 36 35 37

The manager of a motel has 316 rooms. From observation over a long period of time, she knows that on an average night, 268 rooms will be rented. The long-term standard deviation is 12 rooms. For 10 consecutive nights, the following numbers of room were rented each night:

Night 1 2 3 4 5 6 7 8 9 10

Number of Rooms 238 245 261 269 273 250 241 230 215 217

+3σ = 34.3…………………………………………………………………………………………………………

+2σ= 30.1……………………………………………………………………………………………………….

+1σ = 25.9………………………………………………………………………………………………………..

µ = 21.7 _________________________________________________________

-1σ= 17.5………………………………………………………………………………………………………………

-2σ= 13.3………………………………………………………………………………………………………………

-3σ =9.1 ………………………………………………………………………………………………………………

Days 1 2 3 4 5 6 7 8 9 10

+3σ = …………………………………………………………………………………………………………

+2σ= ……………………………………………………………………………………………………….

+1σ ………………………………………………………………………………………………………..

µ = _________________________________________________________

-1σ= ………………………………………………………………………………………………………………

-2σ= ………………………………………………………………………………………………………………

-3σ = ………………………………………………………………………………………………………………

Nights 1 2 3 4 5 6 7 8 9 10

onsider the following data:

UBI POH TLAM

120, 9, 21

60, 5, 16

18, 3, 12

21, 5, 12

85, 7, 17

60, 7, 16

(If you want to check data entry: sample covariance UBI, POH = 61.67; UBI, TLAM = 108.39)

a. What is the least squares linear regression equation when UBI is the dependent variable (Y) are X

variables two?

b. Which of the coefficients, if any, are significantly different from zero at the 90% level?

A researcher is interested in studying how playing video games before bed might influence sleep quality. She randomly assigns 30 teenagers to play video games right before bed for a week, and 30 teenagers to watch TV right before bed for a week, and then compares their sleep quality.

What would be a type I error for this scenario?

What would be a type II error for this scenario?