Question

QUESTION 2 When calculating confidence intervals, how do you determine which formula to use?

Answer 1

Solution -

Generally confidence interval is constructed for mean, standard deviation and proportion. Following image has categorised table for confidence interval for mean, sd and proportion with formulas and minitab software path.

Distribution Minitab Path Formula Z-distribution Mean (o known) Stat > Basic Stat > 1-sample Z > Options u = 7+Zx, T-distribution Mean (o unknown) Stat > Basic Statistics > 1- Sample t u = XI tal2, n- Standard Deviation Chi-squared (X) distribution Stat > Basic Statistics > Display Descriptive Statistics n-1 - SOS Z Z ila/2 Zd, al2 F-distribution Proportion (exact) Stat > Basic Statistics > 1- Proportion afin 12) Power =- lower 12+VF .7. 11-a2(12) Pupper = 2+ViT 1- 12) Z-distribution Proportion (estimate) p= ZcVn p(1-P)

Also a summary formulae table for different condition of parameters.

SUMMARY OF Popice Distr 'n | Diste'n of 100ft-«)% 6.2. FORMULAS Parameter Estimator Disten of Estimator 180114) Gr for marameter cij o hown " N(4,0²) (same as popia) * = 2 h Il ě appr proy. Nu, s [clis unknown larze 22:2 (since Taiga unknown, Small unknown or Mat Morowal (same as poph) Tin large approx (n.) t by CLT voris known the >il or unknown: unknown ciis n Small : unknown Nu, 02) | Nilu, pe l az key: Ex-2)(n-1) X Hunknown or not normal I Isame ( as popin) unknown unknown Bernoulli (p) Bernoulli (*) į p fie. P(x+1)= pl proprio Il p(x=0}= 1-p! º r X Sample lain large : approx propre . by CLT difficult lim Small : difficult

A flow chart for confidence interval of sample mean

Use sample mean How large is Sample n 30 n>30 Distin of X Dist'n of X? Assume normal by CLT. Is pop- normal? no Dist 'n or X is unknown Is the population std. dev. known? Dist'n of sample mean is normal regardless of n. St op! Is the population sta. dev. known?

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