Question

In: Statistics and Probability

Forest City Casino is interest in determining the percentage of their weekend visitors who spend more...

Forest City Casino is interest in determining the percentage of their weekend visitors who spend more than $1,000 at their casino. Based on the sample below, establish a 95% confidence interval for the percentage of weekend customers who spend more than $1,000.

Forest City Casino Weekend Customer Spend Survey
$175 $775 $325 $100 $250 $300 $675 $750 $900 $725 $750
$400 $250 $250 $300 $675 $600 $750 $675 $575 $200 $925
$425 $675 $975 $550 $450 $800 $6,775 $400 $600 $150 $250
$450 $525 $925 $925 $850 $550 $175 $100 $575 $975 $1,225
$825 $225 $425 $925 $600 $475 $850 $850 $725 $225 $275
$800 $350 $750 $500 $825 $2,500 $450 $800 $925 $900 $875
$425 $575 $1,775 $300 $675 $650 $800 $950 $950 $175 $9,125
$875 $375 $425 $125 $300 $275 $350 $325 $4,475 $250 $300
$125 $100 $725 $950 $925 $275 $375 $875 $725 $675 $425
$950 $850 $750 $525 $625 $475 $425 $225 $875 $475 $4,625
$925 $700 $125 $875 $450 $150 $275 $975 $400 $550 $175
$525 $350 $775 $450 $675 $375 $100 $775 $350 $400 $450
$925 $525 $175 $600 $250 $800 $575 $975 $100 $475 $375
$575 $500 $250 $550 $650 $475 $925 $600 $600 $475 $600
$500 $650 $275 $650 $500 $225 $950 $350 $975 $575 $825
$675 $450 $125 $950 $850 $600 $700 $675 $700 $1,925 $800
$925 $450 $350 $675 $7,250 $650 $250 $7,575 $675 $600 $750
$800 $775 $400 $6,625 $750 $800 $175 $350 $350 $275 $125
$150 $875 $275 $350 $325 $625 $350 $400 $700 $200 $600
$450 $175 $475 $800 $950 $825 $125 $950 $800 $950 $925
$150 $150 $125 $550 $725 $825 $600 $200 $500 $225 $925
$700 $875 $100 $900 $550 $900 $375 $850 $475 $8,800 $3,775
$325 $800 $350 $725 $250 $4,075 $100 $750 $450 $575 $825
$125 $725 $4,725 $875 $625 $725 $875 $100 $975 $200 $175
$850 $125 $150 $325 $300 $575 $125 $650 $250 $150 $700

BLANK #1: Is this a question involving mean or proportion? ***ANSWER "MEAN" OR "PROPORTION" (WITHOUT THE QUOTATION MARKS)***

BLANK #2: What is the LOW end of the estimate ***ANSWER TO 2 DECIMALS...FINAL ANSWER IN DOLLARS OR PERCENT FORM (CHOOSE THE APPROPRIATE OPTION FOR YOUR QUESTION)...BE SURE TO INCLUDE UNITS WITH ANSWER...IE. EITHER $12.34 OR 12.34%***

BLANK #3: What is the HIGH end of the estimate ***ANSWER TO 2 DECIMALS...FINAL ANSWER IN DOLLARS OR PERCENT FORM (CHOOSE THE APPROPRIATE OPTION FOR YOUR QUESTION)...BE SURE TO INCLUDE UNITS WITH ANSWER...IE. EITHER $12.34 OR 12.34%***

Solutions

Expert Solution

a)

Proportion

b)

Level of Significance,   α =    0.05          
Number of Items of Interest,   x =   15          
Sample Size,   n =    275          
                  
Sample Proportion ,    p̂ = x/n =    0.055          
z -value =   Zα/2 =    1.960   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0137          
margin of error , E = Z*SE =    1.960   *   0.0137   =   0.0268
                  
95%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.055   -   0.0268   =   0.0277

2.77%

c)


Interval Upper Limit = p̂ + E =   0.055   +   0.0268   =   0.0814

8.14%
                  

Thanks in advance!

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