Question

Testing of two brands of electric toothbrushes show that Crest toothbrushes are faulty in 2 of every 25 tested. The Philips toothbrushes are faulty in 3 of every 45 test. Is there enough evidence to say with 95% confidence that the Crest toothbrushes fail less often than the Philips

Answer #1

For Crest toothbrushes:

n1 = 25, x1 = 2

p̂1 = x1/n1 = 0.08

For Philips toothbrushes:

n2 = 45, x2 = 3

p̂2 = x2/n2 = 0.0667

α = 0.05

Null and Alternative hypothesis:

Ho : p1 = p2

H1 : p1 < p2

Pooled proportion:

p̄ = (x1+x2)/(n1+n2) = (2+3)/(25+45) = 0.0714

Test statistic:

z = (p̂1 - p̂2)/√ [p̄*(1-p̄)*(1/n1+1/n2)] = (0.08 -
0.0667)/√[0.0714*0.9286*(1/25+1/45)] = **0.2075**

p-value :

p-value = NORM.S.DIST(0.2075, 1) = **0.5822**

Decision:

p-value > α, Do not reject the null hypothesis.

Conclusion:

There is not enough evidence to conclude with 95% confidence that the Crest toothbrushes fail less often than the Philips.

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