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One gallon of gas is put into each of 30 test cars. The resulting gas-mileage values of the sample are
computed with mean of 28.5 gallons per mile, and standard deviation of 1.2 miles per gallon. What is the
confidence interval estimate of the mean mileage?




Ask by Bates Reyes. in the United States
Jan 23,2025

Solución de inteligencia artificial de Upstudy

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The 95% confidence interval for the mean mileage is .

Solución

To construct a 95% confidence interval for the mean mileage, we’ll follow these steps:
  1. Given Data:
    • Sample size ( ) = 30
    • Sample mean ( ) = 28.5 miles per gallon (mpg)
    • Sample standard deviation ( ) = 1.2 mpg
  2. Determine the Appropriate Distribution:
    • Since the sample size is moderate ( ) and the population standard deviation is unknown, we’ll use the t-distribution.
  3. Find the Critical t-Value:
    • Degrees of freedom ( ) =
    • For a 95% confidence interval, the critical t-value ( ) ≈ 2.045
  4. Calculate the Margin of Error (ME):
  5. Construct the Confidence Interval:
    Rounding to one decimal place gives approximately .
Final Answer:

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Beyond the Answer

To find the confidence interval for the mean mileage, we can use the formula:
where:
  • is the sample mean (28.5 miles per gallon).
  • is the z-value for a 95% confidence level (approximately 1.96).
  • is the sample standard deviation (1.2 miles per gallon).
  • is the sample size (30 cars).
Calculating the margin of error:
Now we find the interval:
Thus, the confidence interval estimate of the mean mileage is approximately , which rounds to .
So, the correct answer is .

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