Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.80. a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85. (Round your answers to two decimal places.) (b) Compute a 98% CI for true average porosity of another seam based on 17 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.) (c) How large a sample size is necessary if the width of the 95% interval is to be 0.39? (Round your answer up to the nearest whole number.) specimens d) What sample size is necessary to estimate true average porosity to within 0.24 with 99% confidence? (Round your answer up to the nearest whole number.)
In: Statistics and Probability
A service process has three serial stages. The defect percentage at stage one is 7%. The defect percentage at stage two is 13%. And, the defect percentage at stage three is 15%. Use 5 decimals for probabilities and 2 decimals for sigma levels in the following situations. (a)[2] Situation A: the connection logic of the three stages is that a good overall outcome only happens if all three stages individually have good outcomes. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. Using Excel, calculate the corresponding sigma level and make a statement. (b)[2] Situation B: the connection logic of the three stages is that a good overall outcome happens when at least one stage has good outcome. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. Calculate the corresponding sigma level and make a statement. (c)[3] Situation C: the connection logic of the three stages is that a good overall outcome happens when at least two stages individually have good outcomes. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. Calculate the corresponding sigma level and make a statement. (d)[3] Give some possible real‐life processes for the three situations above.
In: Statistics and Probability
Historically, the percentage of residents of a certain country who support laws has been 52%. A recent poll of 987 people showed 531 in favor of laws. Assume the poll was given to a random sample of people. Test the claim that the proportion of those favoring stricter control has changed. Perform a hypothesis test, using a significance level of 0.05.
In: Statistics and Probability
A service process has three serial stages. The defect percentage at stage one is 16%. The defect percentage at stage two is 13%. And, the defect percentage at stage three is 10%. Use 3 decimals for probabilities in the following situations. (a)[2] Situation A: the connection logic of the three stages is that a good overall outcome only happens if all three stages individually have good outcomes. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. (b)[2] Situation B: the connection logic of the three stages is that a good overall outcome happens when at least one stage has good outcome. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. (c)[3] Situation C: the connection logic of the three stages is that a good overall outcome happens when at least two stages individually have good outcomes. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. (d)[3] Give some possible real‐life processes for the three situations above.
In: Statistics and Probability
Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population.) A random sample of six Denver neighborhoods gave the following information: x 29 2 11 17 7 6 y 173 35 132 127 69 53 ?x=72, ?y=589, ?x^2=1340, ?y^2=72,277,?xy=9499 a) draw a scatter diagram for the data b) find x bar, y bar, b and the equation of the least-squares line. Plot the line on the scatter diagram of part (a). c) Find the sample correlation coefficient r and the coefficient of determination. What percentage of the variation in y is explained by the least-squares model? d) Test the claim that the population correlation coefficient p is not zero at the 1% level of significance. e) For a neighborhood with x= 12% change in population in the past few years, predict the change in the crime rate (per 1000 residents) f) verify that Se= 22.5908 g) Find a 80% confidence interval for the change in crime rate when the percentage change in population is x= 12% h) Test the claim that the slope B of the population least-squares line is not zero at the 1% level of significance. I) Find an 80% confidence interval for B and interpret its meaning show all steps and work please for credit
In: Statistics and Probability
The U.S. Census Bureau conducts annual surveys to obtain information on the percentage of the voting-age population that is registered to vote. Suppose that 649 employed persons and 666 unemployed persons are independently and randomly selected, and that 364 of the employed persons and 299 of the unemployed persons have registered to vote. Can we conclude that the percentage of employed workers ( p1 ), who have registered to vote, exceeds the percentage of unemployed workers ( p2 ), who have registered to vote? Use a significance level of α=0.05 for the test.
Step 2 of 6:
Find the values of the two sample proportions, p^1 and p^2. Round your answers to three decimal places.
In: Statistics and Probability
Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.77.
(a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 16 specimens from the seam was 4.85. (Round your answers to two decimal places.)
,
(b) Compute a 98% CI for true average porosity of another seam
based on 12 specimens with a sample average porosity of 4.56.
(Round your answers to two decimal places.)
,
(c) How large a sample size is necessary if the width of the 95%
interval is to be 0.49? (Round your answer up to the nearest whole
number.)
specimens
(d) What sample size is necessary to estimate true average porosity
to within 0.23 with 99% confidence? (Round your answer up to the
nearest whole number.)
specimens
In: Statistics and Probability
| Prepare an analysis of the revenue change, separating the productivity effect (billing percentage) | |||
| from the volume effect (increase in number of consultants). | |||
| Exhibit 4: Budget and Actual Income Statement: Quarter 2 2000 | ||||
| Actual | Budget | |||
| Revenues | $ 3,264,000 | $ 3,231,900 | ||
| Less: | ||||
| Consultants' Salaries and Fringes | $ 2,029,050 | $ 1,748,250 | ||
| Operating Expenses | $ 938,560 | $ 877,300 | ||
| Total Expenses | $ 2,967,610 | $ 2,625,550 | ||
| Operating Profit | $ 296,390 | $ 606,350 | ||
| Profit % | 9.1% | 18.8% | ||
|
Operating Statistics |
||||
| Number of Consultants(FTE) | 113 | 105 | ||
| Hours Supplied | 50,850 | 47,250 | ||
| Hours Billed | 39,000 | 35,910 | ||
| Average Billing Rate | $ 83.69 | $ 90.00 | ||
| Your Solution: | |||||||
| Actual Consultant Hours Supplied | Actual Billing % | Expected Billing % | Expected Billing Rate | Variance Amount | Favorable/ Unfavorable? |
||
| Consultant Billing Percentage | |||||||
| Actual Consultant Hours Supplied | Expected Consultant Hours Supplied | Expected Billing % | Expected Billing Rate | Variance Amount | Favorable/ Unfavorable? |
||
| Consultant Quantity | |||||||
In: Accounting
1. If the original population is normally distributed, will random sample means and random sample percentage have distribution that is also normally distributed? Explain.
2. If the original population is skewed, will random sample means and random sample percentage have a distribution that is also normally distributed? If not, what sample size will ensure that the sampling distribution is normal?
3. State the Central Limit Theorem (one of the most important theorems in statistics.)
4. what are some of the consequences of the central limit theorem and how does it relate to the
In: Statistics and Probability
How many people live on $2 dollars a day or less? What percentage of the world's wealth is owned by the Top 1% of the world's population? And what percentage by the bottom 80%? How can we distinguish between the orthodox economic definition of poverty and the alternative view embraced by the UN Millennium Program? Why should we be especially concerned with female literacy and poverty? What can we expect will happen to the percentage of world living in poverty by 2050 under the most severe environmental forecasts?
In: Economics