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

question 1

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.

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Definitions:

Maturation

The process of becoming mature, involving growth and development that occurs in an organism over time.

Development

The process of growth and change that organisms undergo from their inception to their mature form, including physical, cognitive, and social changes.

Proximal

Describes a position in a limb that is nearer to the point of attachment or to the body trunk.

Lateral

Describing a position or direction toward the side of the body or a body structure, away from the midline.