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. In a random sample of 120 amplifiers from this company, the mean gain is 9.03dB with a sample standard deviation of 0.861 dB. Is this enough evidence to state the amplifiers from this company fail to have the required mean gain of 10 dB?Calculate the value of the t-test statistic. Round your final answer to 2 decimal places.

Answer 1

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  $t = -12.34$

Step-by-step explanation:

From the question we are told that  

    The population mean is  $\mu = 10 \ dB$

     The  sample size is n =  120

      The  sample  mean is $\= x = 9.03$

       The standard deviation is  $\sigma = 0.861 \ dB$

The  null hypothesis is $H_o : \mu = 10 \ dB$

 The alternative hypothesis is  $H_a : \mu \ne 10\ dB$

Generally the test statistics is mathematically represented as

          $t = \frac{\= x - \mu }{ \frac{\sigma}{ \sqrt{n} } }$    

=>         $t = \frac{9.03 -10 }{ \frac{0.861}{ \sqrt{120} } }$  

=>      $t = -12.34$

the p-value  is obtained from the normal distribution table , the value is  

      $p-value = 2 * P(Z > -12.34)$

      $p-value = 2 * 0.00$

      $p-value = 0.00$  

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