it has been reported that the average life for lightbulbs is 4000 hours. Learnin

Question

it has been reported that the average life for lightbulbs is 4000 hours. Learning of this, a plant manager suspects that the temperature conditions have an adverse effect on the life of bulbs. In a test involving 15 bulbs in various locations, the average life was 3882 hours and a standard deviation of 200 hours. assume normal distribution and use 0.025 significance. do the test results support the manager's suspicion? - I believe H1u<4000 but the chegg solution says H1 u is not equal to 4000. Am i wrong or is chegg wrong? If i am wrong, please explain why

Explanation / Answer

Here the claim is, a plant manager suspects that the temperature conditions have an adverse effect on the life of bulbs. Adverse effect means harmful effect so the life of the bulb will get reduced. When it is the case of reducing then it is the case of left-tailed test. You are right here.

Null Hypothesis (H0): µ 4000

Alternative Hypothesis (H1): µ< 4000

You are correct here.

t = ( x bar – Mew)/(s/sqrt(n))

= (3882-4000)/(200/sqrt(15))

= -2.285

The critical value at 0.025 level of significance for 14 degrees of freedom is -2.145.

Here test statistics is less than the critical value (-2.285<-2.145); we reject the null hypothesis.

At 2.5% level of significance there is sufficient evidence to support the manager’s suspicion.

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