Find a 99% confidence interval for the previous problem. (30.19, 32.21) (30.26, 32.14) O (31.195, 31.205) The sample size is too small to find a confidence interval.

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Question 3: find the 99% confidence interval for the previous problem
**Question:**
Find a 99% confidence interval for the previous problem.

**Options:**

1. (30.19, 32.21)
2. (30.26, 32.14)
3. (31.195, 31.205)
4. The sample size is too small to find a confidence interval. 

(Note: Ensure to refer to the context provided in the "previous problem" to select the most appropriate option.)
Transcribed Image Text:**Question:** Find a 99% confidence interval for the previous problem. **Options:** 1. (30.19, 32.21) 2. (30.26, 32.14) 3. (31.195, 31.205) 4. The sample size is too small to find a confidence interval. (Note: Ensure to refer to the context provided in the "previous problem" to select the most appropriate option.)
A car manufacturer produces a new car that advertises an average of 30 MPG. The distribution of MPG of cars is normally distributed. The manufacturer will test 30 cars off the assembly line to find a confidence interval of the average MPG of their new vehicle to determine if it is close to 30. The average MPG of the 30 cars is 31.2 gallons with a standard deviation of 2 gallons. Find a 95% confidence interval for the average MPG of the new vehicle.

Options:

- (30.45, 31.95)
- (30.48, 31.92)
- (31.18, 31.22)
- The sample size is too small to compute a confidence interval.
Transcribed Image Text:A car manufacturer produces a new car that advertises an average of 30 MPG. The distribution of MPG of cars is normally distributed. The manufacturer will test 30 cars off the assembly line to find a confidence interval of the average MPG of their new vehicle to determine if it is close to 30. The average MPG of the 30 cars is 31.2 gallons with a standard deviation of 2 gallons. Find a 95% confidence interval for the average MPG of the new vehicle. Options: - (30.45, 31.95) - (30.48, 31.92) - (31.18, 31.22) - The sample size is too small to compute a confidence interval.
Expert Solution
Step 1

Given information

Sample size (n) = 30

Sample mean = 31.2 gallons

Standard deviation (s) = 2

Significance level (α) = 1 - 0.95 = 0.05

Since, here population standard deviation is unknown therefore using t-distribution.

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