In: Statistics and Probability
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%***
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!
revert back for doubt