A. Redo question 7, but assume that the standard deviation is not known and that

Question

A. Redo question 7, but assume that the standard deviation is not known and that3 lb represents the sample standard deviation. The level of significance is 5%.

B. An auditor is interested in the mean value of a company’s accounts receivable.He randomly samples 200 accounts receivable and finds that the mean accounts receivable is $231. From past experience, he knows that the standard deviationis $25. Use a 0.01 level of significance to test whether the population mean accounts receivable is different from $200.

C. An investment adviser is interested in determining whether a retirement community represents a potential clientele base. Of the 2,000 residents, he randomly samples 100 individuals and finds their mean wealth to be $525,000 with a sample standard deviation of $52,000. Use a 0.10 level of significance to test the hypothesis that the mean wealth is greater than $500,000.

Explanation / Answer

HEre For A part some other data is required so i am doing part (b) and part(c)

Part(b) H0 : = $ 200

Ha : $ 200

Here sample size = 200

sample mean x = $ 231

population standard deviation = $ 25

standard error of the mean = 25/ sqrt(200) = $ 1.7678

Test statistic

Z = ($ 231 - $ 200)/ 1.7678 = 17.54

Here For alpha = 0.01 , Zcritical = 2.575

Z >  Zcritical so we shall reject the null hypothesis and can conclude that population mean accounts receivable different from $ 200.

(c) H0 : = $ 5,00,000

Ha : >  $ 5,00,000

Here sample size = 100

sample mean x = $ 5,25,000

population standard deviation = $ 52,000

standard error of the mean = 52000/ sqrt(100) = $ 5200

Test statistic

Z = (525000 - 500000)/ 5200 = 4.8077

Here at alpha = 0.10 level critical value Zcritical = 1.645

Here, Z >  Zcritical so we shall reject the null hypothesis and can conclude that the mean wealth is greater than $500,000.

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