Anystate Auto Insurance Company took a random sample of 372 insurance claims paid out during a 1-year period. The average claim paid was $1515. Assume σ = $236.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

A sample is selected from a normal population with a µ = 40 and σ = 12. After the treatment is administered to the sample, the sample mean is found to be M = 46. Using two-tailed Z-tests (with p < .05): A) Is there a significant treatment effect if the sample size was n = 4? B) If n = 36? C) What are the 95% confidence intervals for these two situations?

1. Find the SSE for the given data and linear models, and indicate which model gives the better fit.

(0,1) (1,1) (2,2) (4,3)

1. Y = 0.4x + 1.1                                                   SSE = ________
2. Y = 0.5x + 0.9                                                   SSE = ________
3. The better fit is          Y = ____________

2. Given the data

(0,40) (1,60) (2,70) (3,50) (4,60) (5,75) (6,90), (7,80), (8,85)

find:

Sum of x = ______ Sum of y = ______

Sum of  xy = ______ Sum of  x2 = ______ Sum of y2 = _______       

Regression line: ______________________

Correlation Coefficient: ____________

A national survey conducted among a simple random sample of 1513 adults shows that 835 of Americans think the Civil War is still relevant to American politics and the political life.

Conduct a hypothesis test to determine if these data provide strong evidence that the majority of the Americans think the Civil War is still relevant. Give answers to at least 4 decimal places.

A)Identify the claim

B)What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.)
H0:
H1:

C)What test should you run?
2-propZInt
2-propZTest
1-propZTest
1-propZInt

D)Check the conditions for the test are satisfied.

E)Based on the hypotheses, find the following to at least 4 decimal places:

Test Statistic =
p-value =

F)Based on the above we choose to
Accept the null hypothesis
Reject the null hypothesis
Fail to reject the null hypothesis
Accept the alternative hypothesis
G)Interpret your final conclusion in nontechnical terms and address the original claim.

2.Calculate a 95% confidence interval for the proportion of Americans who think the Civil War is still relevant. Give your answer to at least 4 decimal places.

A)Interpret the interval in this context.

B)Does the confidence interval agree with the conclusion of the hypothesis test?

ind the area under the standard normal curve to the left of z=−2.11 z=−2.11 and to the right of z=−0.42 z=−0.42 . Round your answer to four decimal places, if necessary.

Directions: Draw a clearly labeled diagram and then solve each problem.

8. The mean pulse rate for adults is 72 beats per minute (www.healthepic.com) and let’s suppose that the standard deviation is 10. Find:

a. The probability that a randomly chosen adult has a pulse rate over 78 assuming that the rates are normally distributed.

2. The probability that a random sample of 19 adults will have a mean score over 78.

A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms,

15

of them were given multivitamin tablets daily which contain

3

grams of vitamin C and various other vitamins and minerals. The remaining

15

volunteers were given placebo tablets. For each individual, the length of time taken to recover from cold is recorded. At the end of the experiment following data are obtained:

It is known that the population standard deviation of recovery time from cold is

1.8

days when treated with multivitamin, and the population standard deviation of recovery time from cold is

1.5

days when treated with placebo tablets. It is also known that both populations are approximately normally distributed. The researchers claim that the mean recovery time,

μ1

, of the patients treated with multivitamin is not equal to the mean recovery time

μ2

, of the patients who are treated with placebo tablets. At the

0.1

level of significance, is there enough evidence to support this claim? Perform a two-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

Consider the variables y, x1 and x5 from Table B.2 of page 555 in the textbook, regarding Solar Thermal Energy Test Data. Book Linear Regression analysis

1. Construct a normal probability plot of the residuals. does there seem to be any problem with the normality assumption?

2. Construct and interpret a plot of the residuals versus the predicted response.

3. Construct plots of the residuals versus each of the regressor variables. Do these plots imply that regressor is correctly specified?

4. Construct partial regression plots of residuals versus regressors from part c. Discuss the type of information provided by these plots.

5. Compute the studentized residuals and the R−student residuals for this model. What information is conveyed by these scaled residuals?

data

y <- c(271.8, 264,238.8,230.7,251.6,257.9,263.9,266.5,229.1,239.3,258,
257.6,267.3,267,259.6,240.4,227.2,196,278.7,272.3,267.4,254.5,224.7,
181.5,227.5,253.6,263,265.8,263.8)

x1 <- c(783.35, 748.45,684.45,827.8,860.45,875.15,909.45,905.55,756,769.35,793.5,801.65,819.65,808.55,774.95,711.85,694.85,638.1,774.55,757.9,753.35,704.7,
666.8,568.55,653.1,704.05,709.6,726.9,697.15)

x5 <- c(13.2, 14.11,15.68,10.53,11,11.31,11.96,12.58,10.66,10.85,11.41,11.91,12.85,13.58,14.21,15.56,15.83,16.41,13.1,13.63,14.51,15.38,
16.1,16.73,10.58,11.28,11.91,12.65,14.06)

*step by step codes required to compile in R studio, No hand written

A researcher wanted to study the effect of alcohol on reaction time. She hypothesized that alcohol will INCREASE reaction time (participants will take longer to react). She selected a sample of n= 36 participants from Rutgers University. The 36 participants each consumed a 6-ounce glass of wine. Thirty minutes later, the researcher measured each participant’s reaction time, using a standardized driving simulation task for which the regular population has a µ = 400 msec reaction time with a σ = 48. The reaction time mean for the sample was M= 412 msec. Are the data sufficient to conclude that the alcohol significantly increased reaction time?

1. Name the population: ____________________________________

2. Name the sample: ________________________________

3. Cause-What is the independent variable? ___alcohol/ wine________________

4. Effect-What is the dependent variable? ____standardized driving simulation task ____________________

5. What is the appropriate hypothesis test? __________________

6. What two means are you comparing in this test? _____________________________

7. Please calculate the appropriate hypothesis test using all four steps:

Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7,400 copies. The cost of one copy of the book is $11.50. The holding cost is based on an 18% annual rate, and production setup costs are $150 per setup. The equipment with which the book is produced has an annual production volume of 25,000 copies. Wilson has 250 working days per year, and the lead time for a production run is 15 days. Use the production lot size model to compute the following values. (Round your answers to two decimal places.)

(a)

Minimum cost production lot size

(b)

Number of production runs per year

(c)

Cycle time

(d)

Length of a production run (in days)

days

(e)

Maximum inventory

(f)

Total annual cost (in $)

$

(g)

Reorder point

Suppose that Westside Auto, a manufacturer of automobile generators with D = 13,000 units per year, C_h = (2.00) (0.20) = $0.40, and C_o = $25, decided to operate with a backorder inventory policy. Backorder costs are estimated to be $5 per unit per year. Identify the following. (Assume 250 working days per year. Round your answers to two decimal places.)

(a)

Minimum cost order quantity

(b)

Maximum number of backorders

(c)

Maximum inventory

(d)

Cycle time (in days)

days

(e)

Total annual cost (in $)

$

The following data represent the flight time​ (in minutes) of a random sample of seven flights from one city to another city.

282​,

268​,

258​,

264​,

255​,

261,

267

Compute the range and sample standard deviation of flight time.

The range of flight time is_______minutes.

Give an example of a situation in which you believe a Type 1 Error is more serious than a Type II Error. Give an example of situation in which you believe a Type II Error is more serious than a Type 1 Error. In each case, why do you think so?

Calculate 80%, 90% and 99% confidence intervals for the standard deviation. Include here the sample standard deviation and sample size -30pts-

S=

n=

〖χ²〗_R=(chi-square right tail)=

〖χ²〗_L=(chi-square left tail)=

80% confidence interval:

Interpretation:

〖χ²〗_R= 〖χ²〗_L= 90% confidence interval:

Interpretation:

〖χ²〗_R= 〖χ²〗_L= 99% confidence interval:

Interpretation:

How do these confidence intervals relate to the population standard deviation you calculated in question #1, when the set of data was treated as a population? -5 pts-

Use the sample you chose to perform a meaningful hypothesis test for the mean. Include all the assumptions, identify clearly the null and alternate hypotheses, show the method used to test the hypothesis and write a clear conclusion

x ̅=

S=

n=

Assumptions/Claim: -10 pts-

Null Hypothesis H0: -5 pts-

Alternate Hypothesis H1: -5 pts-

Method to Test the Hypothesis: -5 pts-

Hypothesis conclusion: -10 pts-

Sample is: 19 24 8 21 70 45 4 13 482 4 8 4 16 0 16 52 30 42 4 5 143 7 18 109 22 26 0 4702 38 71 376 17

Construct the indicated confidence interval for the population mean μ using the​ t-distribution. Assume the population is normally distributed.

c=0.95, x=12.2​, s=0.85​, n=15

A researcher is interested in studying how smoking affects air pollution in rooms. Air pollution is measured as the amount of suspended particulate matter. A random sample of 14 rooms in homes where there is no smokers, and a random sample of 22 rooms in homes where there is a smoker were selected. Assume that all necessary normality assumptions are met. Below are some summaries:

The researcher wants to test whether the difference in the average air pollution between rooms without and with smokers exceeds 2. Show all steps of the testing procedure.