Question

A random sample of 144 Amazon shoppers who shopped on Cyber Monday showed that the shoppers...

A random sample of 144 Amazon shoppers who shopped on Cyber Monday showed that the shoppers spent an average of $232.16 with a standard deviation of $36.
a.    Find the 95% confidence interval for the average amount spent by all Amazon shoppers who shopped on Cyber Monday


b.   Describe how the Central Limit Theorem conditions for the Sampling Distribution of Means have been met.

Math   Statistics-And-Probability   
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Answer #1

a)

95% Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 144- 1 ) = 1.977
232.16 ± t(0.05/2, 144 -1) * 36/√(144)
Lower Limit = 232.16 - t(0.05/2, 144 -1) 36/√(144)
Lower Limit = 226.229
Upper Limit = 232.16 + t(0.05/2, 144 -1) 36/√(144)
Upper Limit = 238.091
95% Confidence interval is ( 226.229 , 238.091 )

b)

Sample is random sample .

sample size is sufficiently large ( > 30)

The Central Limit Theorem conditions for the Sampling Distribution of Means have been met.

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