Asked by Jimmy Tobin on May 15, 2024
Verified
You want to estimate the average gas price in your city for a litre of regular unleaded gasoline.You take a random sample of prices from 15 gas stations,recording an average cost of $1.27 and a standard deviation of $0.06.Create a 95% confidence interval for the mean price per litre of gas.
A) ($1.23,$1.41)
B) ($1.24,$1.38)
C) ($1.24,$1.30)
D) ($1.21,$1.43)
E) ($1.26,$1.38)
Confidence Interval
A range of values calculated from a set of data so that it is very likely, to a specified probability, that the true parameter of the population is within this range.
Standard Deviation
A statistic that measures the dispersion or variability of a set of data points from their mean.
- Acquire the ability to calculate confidence intervals across varying confidence levels and sample sizes.
- Grasp the employment and determination of confidence intervals within real-life situations.
Verified Answer
MC
martha coffieMay 18, 2024
Final Answer :
C
Explanation :
To create a 95% confidence interval, we need to use a t-distribution with 14 degrees of freedom (n-1=15-1=14) since we don't know the population standard deviation. Using a t-distribution table, we find the t-value to be 2.145.
The formula for a confidence interval is:
(sample mean) +/- (critical value) x (standard error)
where the standard error is the standard deviation divided by the square root of the sample size.
Plugging in our values:
(sample mean) +/- (2.145) x (0.06/sqrt(15))
Calculating:
1.27 +/- 0.054
So the confidence interval is ($1.24, $1.30).
The formula for a confidence interval is:
(sample mean) +/- (critical value) x (standard error)
where the standard error is the standard deviation divided by the square root of the sample size.
Plugging in our values:
(sample mean) +/- (2.145) x (0.06/sqrt(15))
Calculating:
1.27 +/- 0.054
So the confidence interval is ($1.24, $1.30).
Learning Objectives
- Acquire the ability to calculate confidence intervals across varying confidence levels and sample sizes.
- Grasp the employment and determination of confidence intervals within real-life situations.
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