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Hypothesis Testing for population mean

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A flashlight company claims that the new bulb in its heavy duty flashlight will average 246 hours of light. A statistics student decides that he/she wants to test this claim at a 5% level of significance to determine if there is evidence to support the claim. The student randomly selects and tests 15 flashlight bulbs and records how long the bulb lasts until it burns out. Assume the life of a bulb is normally distributed with a standard deviation of 7.4 hours. The data is in the table below:

Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Hrs: 246 224 231 242 237 240 243 236 239 255 256 239 247 231 253

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Solution Summary

The solution consists of all details of conducting a one-sample Z-test for population mean.

Solution Preview

Since the population standard deviation is known to be sigma=7.4 hours, it would be appropriate to conduct a one-sample Z-test.

Null hypothesis Ho: the flashlight will average 246 hours of light
...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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