Mathematics, 27.02.2020 02:46 lavorisjonesjr1

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 720 hours. A random sample of 51 light bulbs as a mean of 701.6 hours with a population standard deviation of 62 hours. At an α=0.05, can you support the company’s claim using the test statistic?

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Answer from: finlchey3860

$z=\frac{701.6-720}{\frac{62}{\sqrt{51}}}=-2.119$

p_v =P(Z

If we compare the p value and the significance level given $\alpha=0.05$ we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is lower then 720 hours at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=701.6$ represent the sample mean

$\sigma=62$ represent the population standard deviation

n=51 sample size

$\mu_o =720$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

p_v represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is at least 720 hours :

Null hypothesis: $\mu \geq 720$

Alternative hypothesis: $\mu < 720$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{701.6-720}{\frac{62}{\sqrt{51}}}=-2.119$

P-value

Since is a left tailed test the p value would be:

p_v =P(Z

Conclusion

Answer from: Quest

answer: plz put a pic in so i can answer it

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

when the line is solid:

it's either < or >

when the line is dashed:

it's either < or >

this > inequality sign means:

greater thanmore thanaboveexceeds

this < inequality sign means:

less thanfewer thanbelow

this > inequality sign means:

greater than/equal tono less thanat leastminimum of

this < inequality sign means:

less than/equal tono more thanat mostmaximum of

about the problem:

since the line is solid, that means it's either < or >

srry i'm not done ! i'll

Which inequality is represented by the graph? which test point holds true for the inequality?

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