A telecommunications equipment manufacturer was receiving complaints about low v
ID: 3155626 • Letter: A
Question
A telecommunications equipment manufacturer was receiving complaints about low volume on long distance calls. Amplifiers are used to boost the signal at various points in the long distance lines. The boosting ability of the amplifiers is called "gain." Amplifiers are designed to have a mean gain of 10 decibels. This means that a 1 dB input singal would be boosted to a 10 dB output signal. A random sample of 120 amplifiers from this company is tested for gain to see if the mean gain is 10 dB. The sample mean is 9.03 dB and the sample standard deviation is 0.861 dB. Is this enough evidence to state the amplifiers from this company fail to have the required mean gain of 10 dB?
The p-value for this hypothesis test is less than 0.0001. Select the correct interpretation of this p-value.
The probability of obtaining a sample mean of 9.03 dB or less if the true mean is less than 10 dB is less than 0.0001.
The probability the true mean is 10 dB is less than 0.0001.
The probability the true mean is less than 10 dB is less than 0.0001.
The probability of obtaining a sample mean of 9.03 dB or less if the true mean is 10 dB is less than 0.0001.
a.The probability of obtaining a sample mean of 9.03 dB or less if the true mean is less than 10 dB is less than 0.0001.
b.The probability the true mean is 10 dB is less than 0.0001.
c.The probability the true mean is less than 10 dB is less than 0.0001.
d.The probability of obtaining a sample mean of 9.03 dB or less if the true mean is 10 dB is less than 0.0001.
Explanation / Answer
Given:
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Frame the hypothesis:
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P value interpretation:
P value is the probability of the null hypothesis to be true. If p value is very small this implies that the chances of null hypothesis to be true are negligible.
The extreme low the P value is , the easier it is to reject the null hypothesis.
The decision rule for P value in hypothesis testing is as follows:
P value < Significance level , Reject the null hypothesis
P vlaue > Significance level, Fail to reject the null hypothesis
[Note: When no significance level is mentioned in the question , the most common value is used as 0.05]
.
Inference:
Since P value 0.0001 < 0.05 , we reject the null hypthesis and conclude that the true population mean is not 10db.
Conclusion:
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