8.1 A Confidence Interval for a Population Standard Deviation, Known or Large Sample Size
The following activities and questions relate to material covered in Chapter 8.1 A Confidence Interval for a Population Standard Deviation, Known or Large Sample Size in Introductory Business Statistics (OpenStax).
Data sets for the following questions are available in Excel: 8.1 Data Sets [XLSX].
Questions
- The Yukon Bureau of Statistics tracked the self-serve fuel price data in Whitehorse from May 2018 to May 19, 2021, (see table below). Assume that the fuel price population distribution of fuel price is normal, and the population standard deviation is known to be $6.50. Construct a 90% confidence interval for the population mean of the fuel price. [1] State the confidence interval.
Whitehorse, Yukon Fuel Price 2018-2019 Date Fuel Price May’ 2018 141.6 Jun’ 2018 144.0 Jul’ 2018 143.9 Aug’ 2018 143.7 Sep’ 2018 143.5 Oct’ 2018 143.6 Nov’ 2018 141.9 Dec’ 2018 124.0 Jan’ 2019 124.5 Feb’ 2019 124.6 Mar’ 2019 131.5 Whitehorse, Yukon Fuel Price 2019-2020 Date Whitehorse Apr’ 2019 137.5 May’ 2019 137.4 Jun’ 2019 137.1 Jul’ 2019 140.9 Aug’ 2019 141.4 Sep’ 2019 142.0 Oct’ 2019 141.8 Nov’ 2019 142.2 Dec’ 2019 142.1 Jan’ 2020 142.1 Feb’ 2020 142.0 - Monthly sales of the motor vehicle and parts dealers in Yukon in 2020 are list in the table below ($1,000). Assume that the population distribution of monthly sales is normal, and the population standard deviation is known to be 2500 in $1,000. Construct a 95% confidence interval for the population mean of monthly sales. [2] State the confidence interval.
Monthly motor vehicle and parts sales in Yukon, 2020 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 10136 10875 12094 9614 15156 16032 17898 15011 13285 15706 13110 12672
Solutions
- [latex]\bar{x}\pm{z}_{\frac{a}{2}}\dfrac{\sigma}{\sqrt{n}}=138.80\pm1.645\dfrac{6.50}{\sqrt{22}}=138.80\pm2.28[/latex]
LCL = 136.52
UCL = 141.08
The population mean of fuel price in Whitehorse from May 2018 to May 19, 2021 is between (LCL) $136.52 and (UCL) $141.08 with 90% confidence. - Sample mean:
[latex]\begin{array}{ll}\bar{x}&=\large{\frac{10136+10875+12094+9614+15156+16032+17898+15011+13285+15706+13110+12672}{12}}\\&=13465.75\end{array}[/latex]
[latex]\bar{x}\pm{z}_{\frac{a}{2}}\dfrac{\sigma}{\sqrt{n}}=13465.75\pm1.96\dfrac{2500}{\sqrt{12}}=13456.75\pm1414.51[/latex]
LCL = $12,051,240
UCL = $14, 880,260
In 2020, the population mean of monthly sales of the motor vehicles and parts dealers in Yukon is between (LCL) $12,051,240 and (UCL) $14, 880,260 with 95% confidence.