Answer:
The t-value is t = 1.65.
Step-by-step explanation:
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
The average length of a flight by regional airlines in the United States has been reported as 464 miles.
This means that the null hypothesis is [tex]H_{0}: \mu = 464[/tex].
Simple random sample of 30 flights by regional airlines were to have a mean of 476.9 miles and a standard deviation of 42.8 miles
This means that [tex]n = 30, X = 476.9, s = 42.8[/tex]. So
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{476.9 - 464}{\frac{42.8}{\sqrt{30}}}[/tex]
[tex]t = 1.65[/tex]
The t-value is t = 1.65.
