A random sample of 16 phone batteries lasted a mean of 500 charge cycles, SD 40 cycles. Using t∗=2.131 (15 df), find a 95% confidence interval for the mean of all such batteries.
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Estimate ± margin: xˉ±t∗⋅ns. We use t∗ because the SD s comes from the sample.
Standard error: ns=1640=440=10 cycles.
Margin of error: t∗× standard error =2.131×10=21.31 cycles.
Go the margin each way from xˉ=500: 500−21.31=478.69 and 500+21.31=521.31.
Traps: 480.4 to 519.6 uses z∗, 414.76 to 585.24 forgets n, and 494.67 to 505.33 divides by n.