Question

In: Statistics and Probability

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.

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