Sample Size Increased Statistics Example

1. Metropolitan Research,
Inc.
Roberto Andrés Castillo Zavala
Ramón Alarcon

2. Problem
 A full-sized car model was experiencing what the
owners of the vehicles felt was early transmission
failure

3. Method
 The Detroit manufacturers collected data from a
transmission repair firm of what mileage the
transmission of these cars were failing
 A sample of 50 vehicles was selected to analyze from
the firm

4. Descriptive Statistics
Mean 73,340.30
Standard Error 3521.21
Median 72705.00
Mode #N/A
Standard Deviation 24,898.72
Sample Variance 619,946,014.05
Kurtosis 0.1671
Skewness 0.2601
Range 113,048
Minimum 25,066.00
Maximum 138,114.00
Sum 3,667,015.00
Count 50
Confidence Level(95.0%) 7,076.14

5. Confidence Interval
 Sigma not known
 Degrees of freedom=49
73,340 +/- 2.010* (24,898.72/50)
73,340 miles ± 7,076 miles
66,264 miles≤ x̄ ≤ 80,416

6. Interpretation
 Based on the 95% confidence interval developed
previously, the expected transmission failure of the
sample population falls within the range of 66,264 miles
to 80,416 miles.

7. The acceptable minimum
 Based on the 95% confidence interval any car that
experiences transmission failure before 66,264 miles
driven should be considered premature transmission
failure.

8. Decreasing ME
 To obtain a margin of error of 5000…
n= (2.010^2)*(24,898.72^2)
(5000^2)
n=101
We have to increase the sample size to 101

9. Additional Information
 Increasing the sample the sample size by 51 will
reduce the margin of error to 5,000, and a smaller
margin of error results in a more accurate confidence
interval. Therefore the larger the sample size we have
at our disposal the closer we can estimate the sample
mean to the population mean. From this data, a more
accurate minimum acceptable mileage for transmission
failure can be established from the lower end of the
confidence interval.