A random sample of mid-sized cars tested for fuel consumption gave a mean of miles per gallon with a standard deviation of miles per gallon.
Assuming that the miles per gallon given by all mid-sized cars have a normal distribution, find a confidence interval for the population mean, .
Round your answers to two decimal places.
Use a confidence interval formula for the data.
Here is an example of one for a 95% confidence interval:
CI95 = mean ± 1.96 (sd/√n)
To find the confidence interval for the population mean, we need the sample mean, sample standard deviation, sample size, and the desired confidence level.
However, you haven't provided the values for the sample mean, sample standard deviation, and sample size. Could you please provide those values so that I can calculate the confidence interval for you?
To find a confidence interval for the population mean, we will use the formula:
Confidence interval = sample mean ± (critical value) * (standard deviation / square root of sample size)
First, we need to determine the critical value based on the desired confidence level. Let's assume the desired confidence level is 95%.
To find the critical value, we can use a standard normal distribution table or a calculator. The critical value for a 95% confidence level is typically denoted by a Z-score of 1.96.
Next, we need to substitute the given values into the formula. Let's assume the sample mean is x̄ = 30 miles per gallon, and the standard deviation is σ = 5 miles per gallon. Also, let's assume the sample size is n = 100 mid-sized cars.
Confidence interval = 30 ± (1.96) * (5 / √100)
Now, we can calculate the confidence interval:
Confidence interval = 30 ± (1.96) * (5 / 10)
Simplifying this expression:
Confidence interval = 30 ± 1.96 * 0.5
Finally, we can calculate the lower and upper bounds of the confidence interval:
Lower bound = 30 - 1.96 * 0.5
Upper bound = 30 + 1.96 * 0.5
Calculating these values:
Lower bound = 30 - 0.98
Upper bound = 30 + 0.98
Rounding these values to two decimal places:
Lower bound = 29.02
Upper bound = 30.98
Therefore, the confidence interval for the population mean is (29.02, 30.98) miles per gallon.