A random sample of six 2009 sports cars is taken and their "in the city" miles per gallon is recorded. The results are as follows: 23 19 24 17 16 22. Assuming the population distribution is normal, calculate the 99% confidence interval for μ, the population mean "in city" mpg for 2009 sports cars.

Hagman7v

Hagman7v

Answered question

2022-09-23

T-Intervals and % Confidence Interval
A random sample of six 2009 sports cars is taken and their "in the city" miles per gallon is recorded. The results are as follows: 23, 19, 24, 17, 16, 22. Assuming the population distribution is normal, calculate the 99% confidence interval for μ, the population mean "in city" mpg for 2009 sports cars.

Answer & Explanation

acorazarxf

acorazarxf

Beginner2022-09-24Added 9 answers

Step 1
1. Calculate the sample mean x ¯ , which is the sum of the data divided by the sample size n = 6.
2. Calculate the sample standard deviation
s x = 1 n 1 i = 1 n ( x i x ¯ ) 2 .
3. Calculate the standard error s x / n
Step 2
4. Find the critical value of the Student's t distribution with n 1 = 5 degrees of freedom corresponding to a 99% confidence interval--this is the 99.5th percentile.
5. The confidence interval margin of error is the critical value t n 1 , α / 2 that you found in step 4 multiplied by the standard error you found in step 3.
6. The desired confidence interval for the population mean μ is [ x ¯ M E , x ¯ + M E ], where ME is the margin of error you found in step 5.

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