Thursday, May 20, 2010

Approximately 5% of U.S. families have a net worth in excess of $1 million and thus can be called "millionaire

1.Approximately 5% of U.S. families have a net worth in excess of $1 million and thus can be called "millionaires." However, a survey in the year 2000 found that 30% of Microsoft's 31,000 employees were millionaires. If random samples of 100 Microsoft employees had been taken that year, what proportion of the samples would have been between 25% and 35% millionaires?





2. Assume that house prices in a neighborhood are normally distributed with standard deviation $20,000. A random sample of 16 observations is taken. What is the probability that the sample mean differs from the population mean by more than $5,000?





3.When determining the sample size necessary for estimating the true population mean, which factor is not considered when sampling with replacement?


a. The population size


b. The population standard deviation


c. The level of confidence desired in the estimate


d. The allowable or tolerable sampling error

Approximately 5% of U.S. families have a net worth in excess of $1 million and thus can be called "millionaire
1. E = (Zα/2)(√[(p(1-p)/n] = 0.05 (5%) This is the proportion that differ from the mean by 30%. Solve for Zα/2.


Zα/2 = 0.05/[√[0.30(0.70)/100] = 0.05/0.0458 = 1.09


The probability associated with Z = 1.09 is 0.138 (answer)





2. E = tα/2(s/√n) = 5000 = (tα/2)(20000/4) Where E is the deviation from the sample mean


Solve for tα/2 = 5000/5000 = 1; the probability associated with t = 1.0 is 0.167 (found in MS-Excel function TDIST(t-value, df, 1)


So the probability that the sample mean differs from the population mean by more than $5,000 is 0.167.





3. (a) The population size. Note the formula in #2.
Reply:So is this your entire homework assignment, or just part of it?


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