Cold start ignition time

Module B+F · freq 14

$\bar{x}\ \pm\ \underbrace{t_{n-1,\;\frac{1+\gamma}{2}}}_{\large Q}\cdot\frac{s}{\sqrt{n}}$

Signals: Given a run of raw data (10–25 values) · a) asks for the average / mean · b) asks for the sample variance · c) asks for a confidence interval for the true mean at some confidence level · d) width written as

2\times Q\times\frac{s}{\sqrt{n}}

; asks what

Q

is and what it's called

Knowledge point:Descriptive statistics →Confidence intervals & proportions →

Generating question…

Method

a) np.mean(x)
b) np.var(x, ddof=1) —— ddof=1 means dividing by $n-1$ for the sample
c) variance unknown → t distribution: tc = stats.t.ppf((1+conf)/2, n-1), CI = m ± tc*s/√n
d) $Q$ is just that t quantile; its name = "the $(1+\gamma)/2$ quantile of $t_{n-1}$ distribution"

Pitfalls where marks are lost

Forgetting ddof=1 → divides by n instead of n−1, everything wrong (MATLAB's std/var default to n−1, so they're actually safe)
Using norm.ppf instead of t.ppf —— if σ is unknown you must use t
Writing the degrees of freedom as n —— it's n−1
Writing the quantile as γ —— it's (1+γ)/2 (98% → 0.99, not 0.98)
b) asks for the variance —— these two question types are exactly opposite, don't answer the wrong one