flying j diesel fuel prices using confidence intervals to estimate a population mean susan and cliff
TRANSCRIPT
Flying J Diesel Fuel Prices
Using Confidence Intervals to Estimate a Population Mean
Susan and Cliff
Objectives
• What’s the difference between a 95% Confidence Interval and a 99% Confidence Interval for estimating a population mean?
• How does sample size influence both the 95% and 99% Confidence Interval for estimating a population mean?
Context
• With rising diesel fuel prices, how does a trucking company make a profit?
• Realistic estimates of the price of diesel fuel could be critically important
Population and Random Sampling
• Database of diesel fuel prices at 167 Flying J truck stops across the continental U.S.
• SPSS – Statistical Package for the Social Sciences
• Use SPSS to create 95% and 99% Confidence Intervals for various sample sizes (n = 10, n = 20, n = 50)
• Demonstrate rossman.chance.com Applet for Confidence Intervals
Descriptives
2.8790 .02902
2.8133
2.9447
2.8801
2.8990
.008
.09177
2.73
3.01
.28
.10
-.391 .687
-.080 1.334
Mean
Lower Bound
Upper Bound
95% ConfidenceInterval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
PRICEStatistic Std. Error
“Based on a sample of 10 cases, I am 95% confident that the population mean diesel fuel price is between $2.81 and $2.94”
“Based on a sample of 10 cases, I am 95% confident that the population mean diesel fuel price is between $2.81 and $2.94”
“Based on a sample of 10 cases, I am 99% confident that the population mean diesel fuel price is between $2.78 and $2.97”
Descriptives
2.8790 .02902
2.7847
2.9733
2.8801
2.8990
.008
.09177
2.73
3.01
.28
.10
-.391 .687
-.080 1.334
Mean
Lower Bound
Upper Bound
99% ConfidenceInterval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
PRICEStatistic Std. Error
“Based on a sample of 10 cases, I am 95% confident that the population mean diesel fuel price is between $2.81 and $2.94”
“Based on a sample of 10 cases, I am 99% confident that the population mean diesel fuel price is between $2.78 and $2.97”
Descriptives
2.8790 .02902
2.7847
2.9733
2.8801
2.8990
.008
.09177
2.73
3.01
.28
.10
-.391 .687
-.080 1.334
Mean
Lower Bound
Upper Bound
99% ConfidenceInterval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
PRICEStatistic Std. Error
“Based on a sample of 10 cases, I am 95% confident that the population mean diesel fuel price is between $2.81 and $2.94”
“Based on a sample of 10 cases, I am 99% confident that the population mean diesel fuel price is between $2.78 and $2.97”
Descriptives
2.8970 .02731
2.8189
2.9751
2.8973
2.8990
.015
.12216
2.66
3.13
.47
.21
-.242 .512
-.492 .992
Mean
Lower Bound
Upper Bound
99% ConfidenceInterval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
PRICEStatistic Std. Error
Descriptives
2.8970 .02731
2.8398
2.9542
2.8973
2.8990
.015
.12216
2.66
3.13
.47
.21
-.242 .512
-.492 .992
Mean
Lower Bound
Upper Bound
95% ConfidenceInterval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
PRICEStatistic Std. Error
“Based on a sample of 20 cases, I am 95% confident that the population mean diesel fuel price is between $2.84 and $2.95”
“Based on a sample of 20 cases, I am 99% confident that the population mean diesel fuel price is between $2.82 and $2.98”
“Based on a sample of 10 cases, I am 95% confident that the population mean diesel fuel price is between $2.81 and $2.94”
“Based on a sample of 10 cases, I am 99% confident that the population mean diesel fuel price is between $2.78 and $2.97”
“Based on a sample of 20 cases, I am 95% confident that the population mean diesel fuel price is between $2.84 and $2.95”
“Based on a sample of 20 cases, I am 99% confident that the population mean diesel fuel price is between $2.82 and $2.98”
Descriptives
2.8792 .01792
2.8432
2.9152
2.8717
2.8790
.016
.12671
2.68
3.20
.52
.17
.736 .337
.167 .662
Mean
Lower Bound
Upper Bound
95% ConfidenceInterval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
PRICEStatistic Std. Error
“Based on a sample of 50 cases, I am 95% confident that the population mean diesel fuel price is between $2.84 and $2.91”
“Based on a sample of 50 cases, I am 99% confident that the population mean diesel fuel price is between $2.83 and $2.93”
Descriptives
2.8792 .01792
2.8312
2.9272
2.8717
2.8790
.016
.12671
2.68
3.20
.52
.17
.736 .337
.167 .662
Mean
Lower Bound
Upper Bound
99% ConfidenceInterval for Mean
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtosis
PRICEStatistic Std. Error
Assessment
• Is a 95% confidence interval larger or smaller than a 99% confidence interval?
• As you increase sample size, both the 95% and the 99% confidence intervals become __________.
Caution
• Applet can be tricky!
