Question

Situación 1: Suponga que 12 ventiladores de alta eficiencia son fabricadas por cierto manufacturero que alega que éstos duran un promedio de 21,100 horas con una desviación estándar de 1,293 horas.   Pruebe la hipótesis nula horas contra la hipótesis nula que horas a un nivel de significancia de 0.01.  

Translation:

Suppose 12 high-efficiency fans are manufactured by a certain manufacturer who claims that they last an average of 21,100 hours with a standard deviation of 1,293 hours. Test the null hypothesis μ = 22,000 hours against the null hypothesis that μ = 22,000 hours at a significance level of 0.01.

Situation 2: En un estudio sobre la efectividad de ciertos ejercicios para reducir el peso, un grupo de 16 personas se matricularon en esos ejercicios durante un mes. Los resultados aparecen en la siguiente tabla.

Translation:
In a study on the effectiveness of certain exercises to reduce weight, a group of 16 people enrolled in those exercises for a month. The results appear in the following table.

weight before	weight after
211	198
180	173
171	172
214	209
182	179
194	192
162	159
182	182
172	166
156	154
185	181
167	164
203	201
183	175
245	230
146	142

Utilice un nivel alfa de 0.01. Determine si los ejercicios son efectivos para reducir el peso.

Translation:

Use an alpha level of 0.01. Determine if the exercises are effective in reducing weight.

Answer Sheet format

Situation #1

Data

Hyphothesis

H_o:

H_a:

Mathematical Model:

Decision:

Conclusion:  

Answer 1

The hypothesis being tested is:

H0: µd = 0

Ha: µd > 0

weight before	weight after	Difference
211	198	13
180	173	7
171	172	-1
214	209	5
182	179	3
194	192	2
162	159	3
182	182	0
172	166	6
156	154	2
185	181	4
167	164	3
203	201	2
183	175	8
245	230	15
146	142	4
	184.563	mean weight before
	179.813	mean weight after
	4.750	mean difference (weight before - weight after)
	4.313	std. dev.
	1.078	std. error
	16	n
	15	df
	4.406	t
	.0003	p-value (one-tailed, upper)

The p-value is 0.0003.

Since the p-value (0.0003) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the exercises are effective in reducing weight.

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