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Vika [28.1K]
3 years ago
5

Values of unemployment​

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Alika [10]3 years ago
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Do you actually mean when?
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The quality-control manager at a compact fluorescent light bulb factory need to determine whether the mean life of a large shipm
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Complete Question:

The mean life of a large shipment of CFLs is equal to 7,500 hours. The population standard deviation is 1,000 hours. A random sample of 64 CFLs indicate a sample life of 7,250  hours.

1. State the Null and Alternative Hypothesis.

2. At the 0.05 level of significance, is there evidence that mean life is different from 7,500 hours.

3. Construct a 95% confidence interval estimate of the population mean life of the CFLs.

4. Compute the p-value and interpret its meaning.

Answer:

-2, (7005, 7450), 0.045

Explanation:

1).

H₀: mean of life shipment is 7500 hours

the hypothesis are outlined as follows

H₀: \mu = 7500

H₁: \mu \neq 7500

where, n = 64, x = 7250, \sigma =1000 hours

Test statistics:

Z = \frac{7250-7500}{\frac{1000}{\sqrt{64}} } \\\\Z = -2

Our conclusion from the above result is that there is sufficient evidence to say that the mean life is different from 7500 hours

2). 95% confidence Interval for the population mean \mu is

[7250-1.96\times \frac{1000}{\sqrt{64}},7250+1.96\times \frac{1000}{\sqrt{64}} ]\\\\(7005,7495)

3).

the p-value is given by

p-value =2P(Z\leq -|z|)\\\\p-value =2P(Z\leq -|2|)\\\\p-value = 0.0455

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