Question

A manufacturer claims that the mean lifetime of its lithium batteries is 1401 hours. A homeowner selects 25 of these batteries and finds the mean lifetime to be 1380 hours with a standard deviation of 81 hours. Test the manufacturer's claim. Use a=0.01. p-value = 0.104 > 0.01; reject the Ho; there is not enough evidence to support the claim. ОА. p-value = 0.207 > 0.01; do not reject the Ho; there is enough evidence to support the claim. ОВ. de la se p-value = 0.104 > 0.01; do not reject the Ho; there is enough evidence to support the claim. Ос. p-value = 0.207 > 0.01; reject the Ho; there is not enough evidence to support the claim. OD.

Answer 1

μ = 1401, n = 25, x = 1380, s = 81, significance level = 0.01, Degrees of freedom: df = n-1 = 24

H₀: μ = 1401, H₁: μ ≠ 1401

Test statistic: t = (x-μ)/(s/n^0.5) = (1380-1401)/(81/25^0.5) = -1.296

p-value (Using Excel function T.DIST.2T(test statistic,df))) = T.DIST.2T(1.296,24) = 0.207

p-value = 0.207 > 0.01, do not reject H₀, there is enough evidence to support the claim (Option B)