Through an examination of class total data from Table II, what would you give as
ID: 3277596 • Letter: T
Question
Through an examination of class total data from Table II, what would you give as an estimation (with an uncertainty) for the mean of the means of all physics lab classes throwing darts this week?
Table II: Exp. Data Statistics Group 1 sd SDM 1 |25.ae/2911 o. 2s I |24422. 21 III |25.89204 0.218 IV 25122O8o.2 | Definitions: I : Bin number N : Number of darts landing in bin . N : Total number of darts in data set . : Average bin number T : Average of the group averages sd : Standard deviation SDM : Standard deviation of the mean TG : Group average bin number NC : Number of groups v 25.25.08 0.3 VI25...22 VII 2448 |218 0.22 E, nyl VIII 24.58 ) 2.12 0.21 'E, Tx(T - T)? sd IX 23caual 0.27 x 24:52248) 0.25 sd SDM = AF sd(I) _ECT, a Class 24.19 2.52 0.08 Table IIa: Overall Statistics F | 24.19 sd(7) o. 39Explanation / Answer
we know that the confidence interval is given as
mean +- z*sd/sqrt(n) , where z = 1.96 , for 95% confidence from the z tables and n = 1000 , 100 darts per group for 10 groups
24.79 +- 1.96*0.43/sqrt(1000) , solving this for 95% , we see that the true mean would lie in the range
24.76 , 24.81
where 1.96*0.43/sqrt(1000) is the uncertainity part with which we have build the confidence interval
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