Name Assignment # 3: Show all steps including the formulas for full credit. Use
ID: 3063387 • Letter: N
Question
Name Assignment # 3: Show all steps including the formulas for full credit. Use the space provided and staple your work. Scratch papers will not be accepted. . A group of young businesswomen wish to open a high fashion boutique in a vacant store but only if the households showed the average income of houscholds in the area is at least $25,500. A random sample following results. $21,000 $23,000 $24,000 $24,000 $22,000 $22,000 $26,000 $26,000 $23,500 $25,000 $22.000 $24.500 Assume the population of incomes is normally distributed. a. Compute the sample mean and the standard deviation b. State the hypotheses for this problem. c. Compute the test statistic d. At 99% compute the p-value and test the hypothesis in b, what is your conclusion? 2 A law enforcement agent believes that at most 90% of the drivers stopped on Saturday nights for speeding are under the influence of alcobol. A sample of 66 drivers who were stopped for speeding on a Saturday night was taken. Eighty seven percent of the drivers in the sample were under the influence of alcohol. a. State the null and alternative hypotheses.Explanation / Answer
QUestion 1
(a) Here sample mean x = $ 23583.33
sample standard deviation s = $ 1635.31
(b) H0 : >= $ 25500
HA: < $ 25500
Where is the average income of the households.
(C)
test statistic
t = (x - 25500)/se0
t = (23583.33 - 25500)/(1635.31/sqrt(12) = -1916.67/472.07 = -4.06
(d) Here p - value = TDIST (t > 4.06; 0.01, 11) = 0.0009 < 0.01
so here we can conclude that mean income of households is less than $ 25,500 so boutique shall not be opened here.
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