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Statistics

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Nov 24, 2024

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The genersl nctation for the confidence level of a confidence interval is 100(1-a)%; for example, for & 95% corfidence interval, o s 05; for & S8'% confidence irterval, @ is .02, The confidence in expressed as - w172 X + a2 =) \ vn v vin/ where Lz 1 16 the t value with ares /2 1o the right unde a t distribution with n-1 degress of freedom, As an sxample, from the picture below for o = 05 and n-1 = 10 degress of freedom, the fix) 04 an | a=.05 100(1-a)% = 031 95% @/2 = 025 T dist. df=10 area=.025 3 & 0 “ml: t.025,10 a;a:OZS & Finite populations aliow us to use 3 100(1-«)% confidence interval for 3 population maan i 10 produce a 100(1-«)% confidence interval for 3 population total. To calculate the 100(1-a )% confider [1-a)%; for example, for a8 95% confidence interval. o 15 .05; for & S8% corfidence interval, a s 02. The confidence interva’ for a populaton mean i based on & sample of size n 15 then > L) . with n-1 degrees of freedom. As an example, from the picture below for @ = .05 and n-1 = 10 degrees of freedom, the confidence Interval for u is | x = 22281~ x + 2.2281- 11 ) sulation mean u to produce & 100 1-a)% confidence mtarval for & population total, To calculate the 100]1-a )% confidence interval for the population total, multiply the lower value Jiation size N and multiply the upper value Finite populations aliow us to use a 100( 1.« )% confidence interval for a population mean u to produce a 100( 1.« )% confidence interval for a population total. To calculate the 100( 1. )% confider » = < x [+ vn of the 100(1-a Y% confidence interval for the population mean x by the population size N and muliply the upper value X + Cus2 = y vn of the 100{ 1+« % confidence interval for the population mean x by the population size N. So the 100 1.1 )% corfidence interval for the popuation total s J » » (W x=tatonr | Nixttarsnr" 1) \ vn | vn In April 2023 an insurance company wanted to estmate the total number of Kias that would be stolen in the Unted States in ol of 2023, To the distress of sutomobile insurance companies, the n Increase was likely due to the TikTok challenge that showed viewers how o steal certan Kia models usng only a screwdriver and a USS cable. The only data available to the insurance company In April 2023 was from the Mghway Loss Data Institute and corsisted of the daily number of Kias stolen on the first 60 days of 2023. The resuits are in this Excel BNle Stalen Kias Question. Use the data in the file to calculate a 59% confidence interval for the total number of Kias stolen in 2023 (use N = 365 days). X lower imit of 99% confidence interva upper imk of 59% confidence Interval.
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