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.

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:

- From the table of standard normal distribution, locate the probability value of 0.95.
- Move left until the first column is reached. Note the value as 1.6
- Move upward until the top row is reached. Note the value as 0.04.
- 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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