Question
Asked Nov 8, 2019
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How large of a sample is required if we want to estimate the mean price of a five year old Corvette within +/- $500 with 90% confidence if the standard deviation is known to be $3100.

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Expert Answer

Step 1

Obtain the critical value at 90% confidence level:

It is given that the standard deviation value is $3,100 and margin of error is 500. The confidence level is 0.90.

The level of significance=(1–0.90)/2=0.005.

The required confidence level from left tail normal table=0.90+0.05=0.95.

Procedure for finding the z-value is listed below:

  1. From the table of standard normal distribution, locate the probability value of 0.95.
  2. Move left until the first column is reached. Note the value as 1.6
  3. Move upward until the top row is reached. Note the value as 0.04.
  4. The intersection of the row and column values gives the area to the two tail of z.

The critical value Z=1.64

Step 2

The sample size is obtained below:

The sample size is 104.

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Zxo п3 E 2 1.64х 3,100 500 = (10.168) 103.388 104

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