Question
In: Statistics and Probability
A researcher wishes to estimate the number of days it takes an automobile dealer to sell...
A researcher wishes to estimate the number of days it takes an automobile dealer to sell a Nissan Sentra. A sample of 50 cars has a mean time on the dealer’s lot of 70 days. Assume the standard deviation for the population is 7.5 days
A) Find the best point estimate of the population mean. ___________(hint: no work needed)
B) Find the 95% confidence interval of the population mean.
Conclusion: We can say with 95% confidence that the population mean is between __________and ____________ days.
Solutions
Expert Solution
Solution :
Given that,
= 70
= 7.5
n = 50
At 99% confidence level the z is ,
= 1 - 95% = 1 - 0.95 =
0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.96
a) Margin of error (E) = Z/2* ( /
= 1.96 * (7.5/
E = 2.08
b) At 95% confidence interval estimate of the population mean is,
- E < 
< + E
70 - 2.08 < < 70 + 2.08
67.92 < < 72.08
We can say with 95% confidence that the population mean is between 67.92 and 72.08 days.
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