Personal income. The Annual Demographic Supplement to the current Population Sur

Question

Personal income. The Annual Demographic Supplement to the current Population Survey interviewed more than 128,000 people mean income Hispanic white males interviewed was $41,798. Is each of the bold numbers a parameter or a statistic? 5. in March 2001. The Census Bureau reports that the of the Hispanic males interviewed was $22,771. The mean income for the non- 6. Auto accidents. The number of accidents per week at a hazardous intersection varies with mean = 2.2 and standard deviation = 1.4. This distribution only takes whole-number values, so it is certainly not Normal. (a) Let be the mean number od accidents per week at the intersection during a year (52 weeks). What is the approximate distribution of ž according to the Central Limit The orem? (b) What is the approximate probability that is less than 27 (e) What is the approximate probability that there are fewer than 100 accidents at the in- tersection in a year? (Hint: Restate this event in terms of t.) 7. Posting fees. Weekly postage expenses for your company have a mea of $325 and a deviation of $54. Your company has allowed for $350 postage per weck in its budget. (a) What is the probability that the average weekly postage expenses for the past 9 months (assume each month has 4 weeks) exceed the budgeted amount of $3507 (b) The recent problems with the stock market are affecting your business and you need to reallocate some of your funds, so you'd like to reduce your postage expenses. What is the probability that your postage for the next week will not exceed $3307

Explanation / Answer

Q.5 A statistic and a parameter are very similar. They are both descriptions of groups, like “50% of dog owners prefer X Brand dog food.” The difference between astatistic and a parameter is that statistics describe a sample. A parameterdescribes an entire population.

SO here both bold numbers are parameter as they describe a population.

Q.6

Mean number of accidents = 2.2

standard deviation of number of accidents = 1.4

(a) Now as per CLT, approximate distribution of sample mean will be normal distribution.

(b) Here estimated mean of sample = 2.2

standard error of the sample mean = 1.4/ sqrt(52) = 0.194

Here, Pr(xbar < 2 ; 2.2 ; 0.194) = ?

Z = (2 - 2.2)/ 0.194 = -1.03

Here p - value for Z = -1.03 is 0.1515

so,  Pr(xbar < 2 ; 2.2 ; 0.194) = 0.1515

(c) Accidents per week = 100/52 = 1.923

so,

Pr(xbar < 1.923 ; 2.2 ; 0.194) = ?

Z = (1.923 - 2.2)/ 0.194 = -1.43

Here p - value for Z = -1.43 is 0.0764

so,  Pr(xbar < 2 ; 2.2 ; 0.194) = 0.0764

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