Write Hypotheses for the Two-Sample T-Test $\mathrm { H } _ { 0 } : \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } = 0$

Short Answer

Write hypotheses for the two-sample t-test.
-A consumer group was interested in comparing the operating time of cordless
Toothbrushes manufactured by two different companies. Group members took a random
Sample of 18 toothbrushes from Company A and 15 from Company B. Each was charged
Overnight and the number of hours of use before needing to be recharged was recorded.
Company A toothbrushes operated for an average of 119.7 hours with a standard deviation
Of 1.74 hours; Company B toothbrushes operated for an average of 120.6 hours with a
Standard deviation of 1.72 hours. Do these samples indicate that Company B toothbrushes
Operate more hours on average than Company A toothbrushes? The correct hypotheses to
Address this question are A. $\mathrm { H } _ { 0 } : \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } = 0$ and $\mathrm { H } _ { \mathrm { A } } : \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } < 0$
B. $\mathrm { H } _ { 0 : } \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } = 0$ and $\mathrm { H } _ { \mathrm { A } : } \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } \neq 0$ .
C. $H _ { 0 : } \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } = 0$ and $\mathrm { H } _ { \mathrm { A } : } \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } > 0$ .
D. $\mathrm { H } _ { 0 : } \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } > 0$ and $\mathrm { H } _ { \mathrm { A } : } \mu _ { \mathrm { A } } - \mu _ { \mathrm { B } } < 0$ .
E. None of the above.