An automotive manufacturer has selected 10 car seats to study the Rockwell hardness of the seat recliner
mechanism. A sample of 8 has an average of 44.795 and a standard deviation of 0.402. At 95% percent confidence
level, what is the interval for the population mean?
To determine the interval for the population mean at a 95% confidence level, you can use the formula for the confidence interval for a population mean:
Confidence Interval = X̄ ± (Z * (σ / √n))
where:
- X̄ is the sample mean
- Z is the z-score for the desired confidence level
- σ is the population standard deviation
- n is the sample size
In this case, the sample mean (X̄) is 44.795, the standard deviation (σ) is 0.402, and the sample size (n) is 8.
To find the z-score for a 95% confidence level, you can use a standard normal distribution table or a statistical calculator. For a 95% confidence level, the z-score is approximately 1.96.
Substituting the values into the formula:
Confidence Interval = 44.795 ± (1.96 * (0.402 / √8))
Now you can calculate the confidence interval:
Confidence Interval = 44.795 ± (1.96 * 0.142)
Confidence Interval = 44.795 ± 0.278
Therefore, the interval for the population mean at a 95% confidence level is approximately (44.517, 45.073).