{"id":274,"date":"2023-01-18T19:49:26","date_gmt":"2023-01-19T00:49:26","guid":{"rendered":"https:\/\/opentextbc.ca\/busstatsancillary\/?post_type=chapter&p=274"},"modified":"2023-02-15T13:32:27","modified_gmt":"2023-02-15T18:32:27","slug":"a-confidence-interval-for-a-population-standard-deviation-known-or-large-sample-size","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/busstatsancillary\/chapter\/a-confidence-interval-for-a-population-standard-deviation-known-or-large-sample-size\/","title":{"raw":"8.1 A Confidence Interval for a Population Standard Deviation, Known or Large Sample Size","rendered":"8.1 A Confidence Interval for a Population Standard Deviation, Known or Large Sample Size"},"content":{"raw":"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<\/a>\u00a0in\u00a0Introductory Business Statistics (OpenStax)<\/em><\/a>.\r\n
Data sets for the following questions are available in Excel: 8.1 Data Sets [XLSX]<\/a>.<\/div>\r\n

Questions<\/h1>\r\n
    \r\n \t
  1. 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. [footnote]Data source: Yukon Bureau of Statistics. (2021). Yukon fuel price survey May 2021<\/em>. https:\/\/yukon.ca\/sites\/yukon.ca\/files\/ybs\/fuel_may21.pdf[\/footnote] State the confidence interval.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Whitehorse, Yukon Fuel Price 2018-2019<\/caption>\r\n
    Date<\/th>\r\nFuel Price<\/th>\r\n<\/tr>\r\n
    May' 2018<\/td>\r\n141.6<\/td>\r\n<\/tr>\r\n
    Jun' 2018<\/td>\r\n144.0<\/td>\r\n<\/tr>\r\n
    Jul' 2018<\/td>\r\n143.9<\/td>\r\n<\/tr>\r\n
    Aug' 2018<\/td>\r\n143.7<\/td>\r\n<\/tr>\r\n
    Sep' 2018<\/td>\r\n143.5<\/td>\r\n<\/tr>\r\n
    Oct' 2018<\/td>\r\n143.6<\/td>\r\n<\/tr>\r\n
    Nov' 2018<\/td>\r\n141.9<\/td>\r\n<\/tr>\r\n
    Dec' 2018<\/td>\r\n124.0<\/td>\r\n<\/tr>\r\n
    Jan' 2019<\/td>\r\n124.5<\/td>\r\n<\/tr>\r\n
    Feb' 2019<\/td>\r\n124.6<\/td>\r\n<\/tr>\r\n
    Mar' 2019<\/td>\r\n131.5<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Whitehorse, Yukon Fuel Price 2019-2020<\/caption>\r\n
    Date<\/th>\r\nWhitehorse<\/th>\r\n<\/tr>\r\n
    Apr' 2019<\/td>\r\n137.5<\/td>\r\n<\/tr>\r\n
    May' 2019<\/td>\r\n137.4<\/td>\r\n<\/tr>\r\n
    Jun' 2019<\/td>\r\n137.1<\/td>\r\n<\/tr>\r\n
    Jul' 2019<\/td>\r\n140.9<\/td>\r\n<\/tr>\r\n
    Aug' 2019<\/td>\r\n141.4<\/td>\r\n<\/tr>\r\n
    Sep' 2019<\/td>\r\n142.0<\/td>\r\n<\/tr>\r\n
    Oct' 2019<\/td>\r\n141.8<\/td>\r\n<\/tr>\r\n
    Nov' 2019<\/td>\r\n142.2<\/td>\r\n<\/tr>\r\n
    Dec' 2019<\/td>\r\n142.1<\/td>\r\n<\/tr>\r\n
    Jan' 2020<\/td>\r\n142.1<\/td>\r\n<\/tr>\r\n
    Feb' 2020<\/td>\r\n142.0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n <\/li>\r\n \t
  2. 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. [footnote]Data source: Yukon Bureau of Statistics. (2020). Yukon retail sales 2020<\/em>. https:\/\/yukon.ca\/sites\/yukon.ca\/files\/ybs\/retail2020.pdf[\/footnote] State the confidence interval.\r\n\r\n\r\n\r\n
    Monthly motor vehicle and parts sales in Yukon, 2020<\/caption>\r\n
    Jan<\/th>\r\nFeb<\/th>\r\nMar<\/th>\r\nApr<\/th>\r\nMay<\/th>\r\nJun<\/th>\r\nJul<\/th>\r\nAug<\/th>\r\nSep<\/th>\r\nOct<\/th>\r\nNov<\/th>\r\nDec<\/th>\r\n<\/tr>\r\n
    10136<\/td>\r\n10875<\/td>\r\n12094<\/td>\r\n9614<\/td>\r\n15156<\/td>\r\n16032<\/td>\r\n17898<\/td>\r\n15011<\/td>\r\n13285<\/td>\r\n15706<\/td>\r\n13110<\/td>\r\n12672<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n<\/ol>\r\n

    Solutions<\/h1>\r\n
      \r\n \t
    1. [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]\r\nLCL = 136.52\r\nUCL = 141.08\r\nThe 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.<\/li>\r\n \t
    2. Sample mean:\r\n[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]\r\n[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]\r\nLCL = $12,051,240\r\nUCL = $14, 880,260\r\nIn 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.<\/li>\r\n<\/ol>","rendered":"

      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<\/a>\u00a0in\u00a0Introductory Business Statistics (OpenStax)<\/em><\/a>.<\/p>\n

      Data sets for the following questions are available in Excel: 8.1 Data Sets [XLSX]<\/a>.<\/div>\n

      Questions<\/h1>\n
        \n
      1. 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]<\/sup><\/a> State the confidence interval.
        \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
        Whitehorse, Yukon Fuel Price 2018-2019<\/caption>\n
        Date<\/th>\nFuel Price<\/th>\n<\/tr>\n
        May’ 2018<\/td>\n141.6<\/td>\n<\/tr>\n
        Jun’ 2018<\/td>\n144.0<\/td>\n<\/tr>\n
        Jul’ 2018<\/td>\n143.9<\/td>\n<\/tr>\n
        Aug’ 2018<\/td>\n143.7<\/td>\n<\/tr>\n
        Sep’ 2018<\/td>\n143.5<\/td>\n<\/tr>\n
        Oct’ 2018<\/td>\n143.6<\/td>\n<\/tr>\n
        Nov’ 2018<\/td>\n141.9<\/td>\n<\/tr>\n
        Dec’ 2018<\/td>\n124.0<\/td>\n<\/tr>\n
        Jan’ 2019<\/td>\n124.5<\/td>\n<\/tr>\n
        Feb’ 2019<\/td>\n124.6<\/td>\n<\/tr>\n
        Mar’ 2019<\/td>\n131.5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
        Whitehorse, Yukon Fuel Price 2019-2020<\/caption>\n
        Date<\/th>\nWhitehorse<\/th>\n<\/tr>\n
        Apr’ 2019<\/td>\n137.5<\/td>\n<\/tr>\n
        May’ 2019<\/td>\n137.4<\/td>\n<\/tr>\n
        Jun’ 2019<\/td>\n137.1<\/td>\n<\/tr>\n
        Jul’ 2019<\/td>\n140.9<\/td>\n<\/tr>\n
        Aug’ 2019<\/td>\n141.4<\/td>\n<\/tr>\n
        Sep’ 2019<\/td>\n142.0<\/td>\n<\/tr>\n
        Oct’ 2019<\/td>\n141.8<\/td>\n<\/tr>\n
        Nov’ 2019<\/td>\n142.2<\/td>\n<\/tr>\n
        Dec’ 2019<\/td>\n142.1<\/td>\n<\/tr>\n
        Jan’ 2020<\/td>\n142.1<\/td>\n<\/tr>\n
        Feb’ 2020<\/td>\n142.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

         <\/li>\n

      2. 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]<\/sup><\/a> State the confidence interval.
        \n\n\n\n\n
        Monthly motor vehicle and parts sales in Yukon, 2020<\/caption>\n
        Jan<\/th>\nFeb<\/th>\nMar<\/th>\nApr<\/th>\nMay<\/th>\nJun<\/th>\nJul<\/th>\nAug<\/th>\nSep<\/th>\nOct<\/th>\nNov<\/th>\nDec<\/th>\n<\/tr>\n
        10136<\/td>\n10875<\/td>\n12094<\/td>\n9614<\/td>\n15156<\/td>\n16032<\/td>\n17898<\/td>\n15011<\/td>\n13285<\/td>\n15706<\/td>\n13110<\/td>\n12672<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n

        Solutions<\/h1>\n
          \n
        1. [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]
          \nLCL = 136.52
          \nUCL = 141.08
          \nThe 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.<\/li>\n
        2. Sample mean:
          \n[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]
          \n[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]
          \nLCL = $12,051,240
          \nUCL = $14, 880,260
          \nIn 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.<\/li>\n<\/ol>\n
          1. Data source: Yukon Bureau of Statistics. (2021). Yukon fuel price survey May 2021<\/em>. https:\/\/yukon.ca\/sites\/yukon.ca\/files\/ybs\/fuel_may21.pdf ↵<\/a><\/li>
          2. Data source: Yukon Bureau of Statistics. (2020). Yukon retail sales 2020<\/em>. https:\/\/yukon.ca\/sites\/yukon.ca\/files\/ybs\/retail2020.pdf ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":123,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-274","chapter","type-chapter","status-publish","hentry"],"part":92,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/274","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/users\/123"}],"version-history":[{"count":12,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/274\/revisions"}],"predecessor-version":[{"id":362,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/274\/revisions\/362"}],"part":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/parts\/92"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/274\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/media?parent=274"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapter-type?post=274"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/contributor?post=274"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/license?post=274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}