Explain Monte Carlo Sampling? Under what circumstances, can it be used? Elaborate on the application and limitations related to this sampling?

Given the follow data for two pooled samples, calculate %95 confidence interval for each

mean, 95% confidence interval for difference of means, and one-tailed p-value for the null hypothesis, “Y

not greater than X”.

a. sample X: n=12, mean = 20.0, std. deviation = 3.1

sample Y: n = 12, mean = 22.0, std. deviation = 3.1

b. Same as part a, except the mean of Y is 23.0

c. Same as part a, except the standard deviation of Y is 4.0

d. Same as part a, except sample size of Y is 20

a dentist wants to find out the average time taken by her hygienist for x rays and clean teeth for patients. she recorded the time to serve 24 randomly selected patients . construct a 99% confidence interval for the average time taken

Mean number of desks produced per week is 42 and population standard deviation is 4.67. the company has introduced new production methods. A random sample of 12 weeks production indicates 44 desks were produced each week. has the introduction of new production methods increased average number of desks produced each week at .05 significance level. Estimate the 95% confidence interval

In an effort to promote a new product, a marketing firm asks participants to rate the effectiveness of ads that varied by length (short, long) and by type of technology (static, dynamic, interactive). Higher ratings indicated greater effectiveness.

(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Assume experimentwise alpha equal to 0.05.)

The data below shows the sugar content in grams of several brands of​ children's and​ adults' cereals. Create and interpret a​ 95% confidence interval for the difference in the mean sugar​ content, μC−μA. Be sure to check the necessary assumptions and conditions.​ (Note: Do not assume that the variances of the two data sets are​ equal.)

Children's cereal:

40.2, 59.4, 47.3, 43.1, 51.5, 48.4, 54.8, 44.3, 41.6, 42, 45.5, 42.7, 37.8, 59.9, 48, 54.1, 38.9, 55.5, 42.8, 34.9

​Adults' cereal: 23.7, 25.3, 2.5, 8.7, 2.4, 21.4, 16.2, 14.4, 23.1, 7.4, 5.9, 12.8, 16.3, 10.8, 1.3, 16.4, 2.2, 4.5, 2.6, 9.7, 12.2, 4.5, 4, 1.4, 6.9, 0.1, 18.8, 6.9, 19.1, 13

A) The confidence interval is (___,___) round to two decimal places

B) Based on these samples, with 95% confidence, children's cereals average between the lower boundary of ___ and upper boundary of ___ more grams of sugar content than adults cereals. (round to two decimal places).

Sociologists say that 90% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that ten married women are having coffee together one morning. Find the following probabilities. (Round your answers to three decimal places.)

(a) all of them dislike their mother-in-law

(b) none of them dislike their mother-in-law

(c) at least eight of them dislike their mother-in-law

(d) no more than seven of them dislike their mother-in-law

The Daily Show. A 2010 Pew Research foundation poll indicates that among 1,099 college graduates, 33% watch The Daily Show. Meanwhile, of the 1,110 people in the poll with a high school degree but no college degree, 22% watch The Daily Show. A 95% confidence interval for pCollegeGrad−pHighSchoolpCollegeGrad−pHighSchool, where pp is the proportion of those who watch The Daily Show, is (0.07, 0.15). Based on this information, determine if the following statements are true or false, and explain your reasoning if you identify the statement as false.

1. At the 5% significance level, the data provide convincing evidence of a difference between the proportions of college graduates and those with a high school degree or less who watch The Daily Show.  ? True False

2. We are 95% confident that 7% less to 15% more college graduates watch The Daily Show than those with a high school degree or less.  ? True False

3. 95% of random samples of 1,099 college graduates and 1,110 people with a high school degree or less will yield differences in sample proportions between 7% and 15%.  ? True False

4. 90% confidence interval for pCollegeGrad−pHighSchoolpCollegeGrad−pHighSchool would be wider.  ? True False

5. A 95% confidence interval for pHighSchool−pCollegeGradpHighSchool−pCollegeGrad is (-0.15,-0.07).  ? True False

A chemical engineer is investigating the effect of process operating temperature on product yield.The study results in the following data:

You can use Minitab to answer the following questions. However, you should be able to calculate the slope and intercept of the least squares regression model by hand, which requires only the means and standard deviations of X and Y, and the correlation coefficient (here r = 0.9763).

1. what is the mean temperature?
130
155
140
145

2. what is the mean yield?
89.6555
90.7380
91.6321
91.6321
       
3. what is the standard deviation of temperature?
900.1573
30.2765
21.4653
101.5487
       
4. what is the standard deviation of yield?
460.7586
601.5487
21.4653
30.2765
       
5. The slope of the fitted regression line is closest to:
-9.6310
191.1070
82.1912
0.6922
207.8088
   
6. The intercept of the fitted regression line is closest to:
191.1070
82.1912
207.8088
-9.6310
   
7. The yield predicted by the regression model for a temperature of 150 degrees is closest to:
-1443.9578
80.355
90.738
94.199
97.66
       
8. The residual error for a temperature of 150 degrees is closest to:
-97.95
99
-3.7510
1
3.7510
97.95
   
9. If the yield were measured in ounces instead of grams (note that 1 gram is 0.35274 ounces), the slope would change by a factor of:
0.35274
1/0.35274
would not change
None of the above
       
10. If the yield were measured in ounces instead of grams (note that 1 gram is 0.35274 ounces), the correlation coefficient would increase by a factor of:

0.35274
1/0.35274
would not change
None of the above

This is a written, statistical report, not simply a collection of different types of Excel output. It is not necessary to include the formulas you used or a copy of the dataset. When answering the questions, make sure to include any relevant statistics and/or the results of your calculations. Like any other written report, you will want to start with an introductory paragraph or problem statement and finish with a conclusion that summarizes the information presented.

1. Use descriptive statistics to summarize the data.

2. Develop a 95% confidence interval estimate of the mean age of unemployed individuals in Philadelphia.

3. Conduct a hypothesis test to determine whether the mean duration of unemployment in Philadelphia is greater than the national mean duration of 14.6 weeks. Use a .01 level of significance. What is your conclusion?

4. Is there a relationship between the age of an unemployed individual and the number of weeks of unemployment? Explain.

2. Blood pressure is independent of the blood group. We want to know, if the distributions attending to the blood group, in three referred samples attending to the type of blood pressure, they are distributed in the same way. To this end, a sample of 1500 subjects was collected and their blood group was determined and blood pressure was taken, classifying it as low, normal, and high. Obtaining the following results:

Use alfa at 0.05

You may need to use the appropriate appendix table or technology to answer this question.

A simple random sample with

n = 54

provided a sample mean of 23.5 and a sample standard deviation of 4.4. (Round your answers to one decimal place.)

(a)

Develop a 90% confidence interval for the population mean.

to

(b)

Develop a 95% confidence interval for the population mean.

to

(c)

Develop a 99% confidence interval for the population mean.

According to the sixth annual survey of employees of advertising agencies, carried out by the company Altschuler, Melvoin & Glasser, these employees can wait another excellent year for their compensation (Adveertising Age, December 1, 1997). To investigate if there is any difference in the annual compensation of artistic directors, suppose you select a random sample of 10 of them from each of four regions: West, South, North and Northeast, and what you want to do the research with 10% of error range.

In what ways do advertisers in magazines use sexual imagery to appeal to youth? One study classified each of 1509 full-page or larger ads as "not sexual" or "sexual," according to the amount and style of the dress of the male or female model in the ad. The ads were also classified according to the target readership of the magazine. Here is the two-way table of counts.

(a) Summarize the data numerically and graphically. (Compute the conditional distribution of model dress for each audience. Round your answers to three decimal places.)

(b) Perform the significance test that compares the model dress for the three categories of magazine readership. Summarize the results of your test and give your conclusion. (Use α = 0.01. Round your value for χ² to two decimal places, and round your P-value to four decimal places.)

Conclusion

Fail to reject the null hypothesis. There is significant evidence of an association between target audience and model dress.Reject the null hypothesis. There is significant evidence of an association between target audience and model dress.    Fail to reject the null hypothesis. There is not significant evidence of an association between target audience and model dress.Reject the null hypothesis. There is not significant evidence of an association between target audience and model dress.

(c) All of the ads were taken from the March, July, and November issues of six magazines in one year. Discuss this fact from the viewpoint of the validity of the significance test and the interpretation of the results.

This is not an SRS. This gives us no reason to believe our conclusions are suspect.This is an SRS. This gives us reason to believe our conclusions might be suspect.    This is not an SRS. This gives us reason to believe our conclusions might be suspect.This is an SRS. This gives us no reason to believe our conclusions are suspect.

6. The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Price in Dollars 135 138 163 168 192

Number of Bids    11    12   15 17 19

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6: Find the estimated value of y when x=163. Round your answer to three decimal places.

Step 4 of 6: Determine the value of the dependent variable yˆ at x=0.

b0, or b1, or x, or y.

Step 5 of 6: Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.