SOLUTION: Hello! I have a question regarding confidence interval estimates. The question reads A: "A Simple Random Sample (SRS) of 40 inner city gas stations shows a mean price for un

Question 301753: Hello! I have a question regarding confidence interval estimates. The question reads
A: "A Simple Random Sample (SRS) of 40 inner city gas stations shows a mean price for unleaded gasoline to be $2.45 with a standard deviation of $0.05, while a SRS of 120 suburban gas stations shows a mean of $2.58 with a standard deviation of $0.08. Construct 95% confidence interval estimates for the mean price of regular gas in inner city and suburban stations."
B: Explain why the interval for the inner city stations is wider then the interval for the suburban stations, even though the standard deviation for the inner city is smaller.
C: Based upon your answer in Part A, are you confident that the mean price of inner city gas is less than $2.50? Explain.
I attempted to solve this problem. I used the margin of era formula. I identified the mean for inner city as 2.45, with a standard deviation of .05 and the confidence interval was 1.96. Suburban mean was 2.58, with a standard deviation of .08 and a confidence interval of 1.96.
Step by step process:
Inner City: 1.96 times .05 divided by the square root of 40 = .015
Suburban: 1.96 times .08 divided by the square root of 120= .014
Is this information correct? I feel as if I did something wrong, the numbers do not look right.
Answer for Part A: Inner City= .015 , Suburban= .014
Answer for Part B:The interval for Inner city is wider because of a smaller sample size.
Answer for Part C: Yes, because the highest price of gas in the inner city would be $2.47 (I took the mean and added .015 to it.)
I would like you to review this question, just to make sure I did this correctly. This grade is quite important, and I am trying my hardest! Thank you so much!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A: "A Simple Random Sample (SRS) of 40 inner city gas stations shows a mean price for unleaded gasoline to be $2.45 with a standard deviation of $0.05,
---
sample mean = 2.45
standard error = invT(0.975 with df=39)*0.05/sqrt(40) = 0.016
95% CI: 2.45-0.016 < u < 2.45+0.016
---
2.43 < u < 2.47
========================================
an SRS of 120 suburban gas stations shows a mean of $2.58 with a standard deviation of $0.08.
sample mean = 2.58
standard error = invT(0.975 with df = 121)*0.08/sqrt(120) = 0.0145
95% CI: 2.58 - 0.0145 < u < 2.58+0.145
2.57 < u < 2.73
=========================================

B: Explain why the interval for the inner city stations is wider then the interval for the suburban stations, even though the standard deviation for the inner city is smaller.
Your answer looks good.
-----------
C: Based upon your answer in Part A, are you confident that the mean price of inner city gas is less than $2.50? Explain.
Ans:; 95% confident
=====================
Cheers,
Stan H.
=====================

I attempted to solve this problem. I used the margin of era formula. I identified the mean for inner city as 2.45, with a standard deviation of .05 and the confidence interval was 1.96. Suburban mean was 2.58, with a standard deviation of .08 and a confidence interval of 1.96.
Step by step process:
Inner City: 1.96 times .05 divided by the square root of 40 = .015
Suburban: 1.96 times .08 divided by the square root of 120= .014
Is this information correct? I feel as if I did something wrong, the numbers do not look right.
Answer for Part A: Inner City= .015 , Suburban= .014
Answer for Part B:The interval for Inner city is wider because of a smaller sample size.
Answer for Part C: Yes, because the highest price of gas in the inner city would be $2.47 (I took the mean and added .015 to it.)

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