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

Answer 1

Explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 10

For the alternative hypothesis,

µ < 10

Since no population standard deviation is given, the distribution is a student's t.

Since n = 120

Degrees of freedom, df = n - 1 = 120 - 1 = 119

t = (x - µ)/(s/√n)

Where

x = sample mean = 9.03

µ = population mean = 10

s = samples standard deviation = 0.861

t = (9.03 - 10)/(0.861/√120) = - 12.34

Assuming a 0.05 significant level,

we would determine the p value using the t test calculator. It becomes

p = 0.00001

Since alpha, 0.05 > than the p value, 0.00001, then we would reject the null hypothesis. Therefore, At a 5% level of significance, there is enough evidence to state the amplifiers from this company fail to have the required mean gain of 10 dB