Answer:
<em>a)95% confidence intervals for the population mean of light bulbs in this batch</em>
(325.5 ,374.5)
b)
<em>The calculated value Z = 4 > 1.96 at 0.05 level of significance</em>
<em>Null hypothesis is rejected </em>
<em>The manufacturer has not right to take the average life of the light bulbs is 400 hours.</em>
Step-by-step explanation:
Given sample size n = 64
Given mean of the sample x⁻ = 350
Standard deviation of the Population σ = 100 hours
The tabulated value Z₀.₉₅ = 1.96
<em>95% confidence intervals for the population mean of light bulbs in this batch</em>
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![(350 -24.5, 350 +24.5)](https://tex.z-dn.net/?f=%28350%20-24.5%2C%20350%20%2B24.5%29)
(325.5 ,374.5)
b)
<u><em>Explanation</em></u>:-
Given mean of the Population μ = 400
Given sample size n = 64
Given mean of the sample x⁻ = 350
Standard deviation of the Population σ = 100 hours
<u><em>Null hypothesis</em></u> : H₀:The manufacturer has right to take the average life of the light bulbs is 400 hours.
μ = 400
<u><em>Alternative Hypothesis: H₁:</em></u> μ ≠400
<u><em>The test statistic </em></u>
![Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7Bx%5E%7B-%7D-mean%20%7D%7B%5Cfrac%7BS.D%7D%7B%5Csqrt%7Bn%7D%20%7D%20%7D)
![Z = \frac{350 -400}{\frac{100}{\sqrt{64} } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B350%20-400%7D%7B%5Cfrac%7B100%7D%7B%5Csqrt%7B64%7D%20%7D%20%7D)
|Z| = |-4|
The tabulated value Z₀.₉₅ = 1.96
The calculated value Z = 4 > 1.96 at 0.05 level of significance
Null hypothesis is rejected.
<u><em>Conclusion:</em></u>-
The manufacturer has not right to take the average life of the light bulbs is 400 hours.