A manufacturer of cordless electric shavers sampled 13 from a day's production and found the mean time of continuous usage without recharging to be 410 minutes with a Sample standard deviation of 30 minutes. We can assume that times are normally Distributed. We wish to test if the true mean operating time without recharging is more Than 400 minutes. The correct null and alternative hypotheses are A) $\mathrm { H } _ { 0 } : \mu = 400 ; \mathrm { H } _ { \mathrm { A } } : \mu 400$ C) $\mathrm { H } _ { 0 } : \mu 400 ; \mathrm { H } _ { \mathrm { A } } : \mu = 400$ D) $\mathrm { H } _ { 0 } : \mu

Question

A manufacturer of cordless electric shavers sampled 13 from a day's production and found the mean time of continuous usage without recharging to be 410 minutes with a Sample standard deviation of 30 minutes. We can assume that times are normally Distributed. We wish to test if the true mean operating time without recharging is more Than 400 minutes. The correct null and alternative hypotheses are A) $\mathrm { H } _ { 0 } : \mu = 400 ; \mathrm { H } _ { \mathrm { A } } : \mu < 400$ B) $\mathrm { H } _ { 0 } : \mu = 400 ; \mathrm { H } _ { \mathrm { A } } : \mu > 400$ C) $\mathrm { H } _ { 0 } : \mu > 400 ; \mathrm { H } _ { \mathrm { A } } : \mu = 400$ D) $\mathrm { H } _ { 0 } : \mu < 400 ; \mathrm { H } _ { \mathrm { A } } : \mu = 400$ E) $\mathrm { H } _ { 0 } : \mu = 400 ; \mathrm { H } _ { \mathrm { A } } : \mu \neq 400$

Quizplus · Accepted Answer

The null hypothesis should always be the opposite of what is being tested in the alternative hypothesis. Here, since we are testing if the true mean operating time without recharging is more than 400 minutes, the null hypothesis should be that the mean operating time is equal to 400 minutes. Therefore, the correct null and alternative hypotheses are: 
H0: μ = 400 
HA: μ > 400 
Option B matches these conditions.

A Manufacturer of Cordless Electric Shavers Sampled 13 from a Day's