Answer:
There is sufficient evidence to state that the amplifiers from this company fail to have the required mean gain of 10 dB
The test statistics is [tex]t = -12.34[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 10 \ dB[/tex]
The sample size is n = 120
The sample mean is [tex]\= x = 9.03[/tex]
The standard deviation is [tex]\sigma = 0.861 \ dB[/tex]
The null hypothesis is [tex]H_o : \mu = 10 \ dB[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 10\ dB[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma}{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{9.03 -10 }{ \frac{0.861}{ \sqrt{120} } }[/tex]
=> [tex]t = -12.34[/tex]
the p-value is obtained from the normal distribution table , the value is
[tex]p-value = 2 * P(Z > -12.34)[/tex]
[tex]p-value = 2 * 0.00[/tex]
[tex]p-value = 0.00[/tex]
given that the p-value is zero which implies that ot would be less than an level of significance it is tested against hence the null hypothesis is rejected
So we can conclude that there is sufficient evidence to state that the amplifiers from this company fail to have the required mean gain of 10 dB
