The Boston Bulb Company produces high-cost bulbs for expensive projection equipment. Johnson, the CEO, claims that...

The Boston Bulb Company produces high-cost bulbs for expensive projection equipment. Johnson, the CEO, claims that a particular bulb type has an average life of at least 600 hours.

Fourteen of these bulbs were randomly selected and tested. The number of hours each bulb lasted was:

614,598,585,572,599,605,604,590,609,606,595,592,601,592

At the significance level, test Johnson's claim about the life of the bulbs.

Solutions

Expert Solution

Here let X be the random variable denoting the life of the bulb
Here X follows normal distribution with mean and standard deviation
The mean is given by=597.28
The standard deviation is given by
s==10.80
HYPOTHESIS TO BE TESTED IS GIVEN BY
H0: Here let the null hypothesis be that average life of bulb is equal to 600 hours.
Let the alternate hypothesis be that the average life of bulb is greater than 600 hour.
H0:600 vs H1:600
TEST STATISTICS IS GIVEN BY
=-0.9423
CONCLUSION
The upper and lower critical value at 5% significant level is 1.771
The test statistics obtained is lies in the upper and lower critical value.
Hence we do have enough evidence to reject the null hypothesis.
Hence we conclude that the average battery life of bulb is 600 hours.

orchestra answered 1 year ago

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