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March 15th, 2010, 02:59 PM   #1
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2 practice statistics questions

I need help on these two questions...its hard to understand what to look for...can anyone do the steps for me, it will help a lot thanks.

1. An SRS of 40 inner city gas stations shows a mean price for regular unleaded gasonline to be $1.45 with a standard devition of $0.05, whilean SRS of 120 suburban stations shows a mean of $1.38 with a standard deviation of $0.08.
a) Construct 95% confidence interval estimates for the mean price of regular gas in inner city and in suburban stations.
b) The confidence interval for the inner city stations is wider than the interval for the suburban stations even though the standard deviation for inner city stations is less than thatfor suburban stations. Explain why this happened.
C)Based on your answer in part a, are you confident that the mean price of inner city gasoline is less than $1.50? Explain.

2. Big Town Fisheries recently stocked a new lake in a city park with 2000 fish of various sizes. The distribution of the lengths of these fish is approximately normal.
a) Big Town Fisheries claims that th mean length of the fish is 8 inches. If the claim is true, which of the following would be more likely?
- A random sample of 15 fish having a mean length that is greater than 10 inches
or
- A random sample of 50 fish having a mean length that is greater than 10 inches
Justify your answer.
b) Suppose the standard deviation of the sampling distribution of the sample mean for random samples of size 50 is 0.3 inch. If the mean length of the fish is 8 inches, use the nrmal distribution to compute the probability that a random sample of 50 fish will have a mean length less than 7.5 inches.
c) Suppose the distribution of fish lengths in this lake was nonnormal but had the same mean and standard deviation. Would it still be approprate to use the normal distribution to compute the probability in part (b)?
Justify your answer.

Thanks a lot
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