Question

You run out of avocados for your daily avocado toast and you need to resupply. However, you are low on funds and decide to search for average prices of avocados. You discover the following prices (in dollars) for a bushel of avocados:

Price of Bushel ($)
8
11
9
8
10
11
10
6
11
6

Use the data to complete the information below (round to two decimals when appropriate)

RANGE =
SS =
VARIANCE =
STANDARD DEVIATION =
est. σ2 =

Suppose you found out that the average price of a bushel of avocados in the united states is $8, with a standard deviation of $1.95.   Your neighbor wants to sell you his bushel for $7. Are you getting an extraordinary deal from your neighbor?

To answer this, calculate the z score for your neighbor's price and find the probability of getting a price lower than that.

z =  round to two decimal places

p =  do not round

Answer 1

X	(X - X̄)²
8	1.00
11	4.00
9	0.00
8	1.00
10	1.00
11	4.00
10	1.000
6	9.000
11	4.000
6	9.000

	X	(X - X̄)²
total sum	90	34.00
n	10	10

RANGE =   11   -   6   =   5

SS =   34.
VARIANCE =Σ(X - X̄)²/(n-1)=   34.0000   /   9   =   3.778
  
STANDARD DEVIATION =   √ [ Σ(X - X̄)²/(n-1)] =   √   (34/9)   =       1.9437

Ho :   µ =   7                  
Ha :   µ <   7       (Left tail test)          
                          
Level of Significance ,    α =    0.05                  
population std dev ,    σ =    1.9500                  
Sample Size ,   n =    10                  
Sample Mean,    x̅ =   8.0000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   1.9500   / √    10   =   0.6166      
Z-test statistic= (x̅ - µ )/SE = (   8.000   -   7   ) /    0.6166   =   1.62
                          
critical z value, z* =       -1.6449   [Excel formula =NORMSINV(α/no. of tails) ]              
                          
p-Value   =   0.9476   [ Excel formula =NORMSDIST(z) ]              
Decision:   p-value>α, Do not reject null hypothesis                       

Yes you are getting extraordinary deal.   

THANKS

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