Question

The average length of a flight by regional airlines in the United States has been reported as 464 miles. If a 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, what would be the test statistics (t-value) if we are to test whether this tend to cast doubt on the reported average of 464 miles or not

Answer 1

The t-value is t = 1.65.

Explanation:

The test statistic is:

`t = (X - \mu)/((s)/(√(n)))`

In which X is the sample mean,
`\mu` is the value tested at the null hypothesis,
`\sigma` 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
`H_(0): \mu = 464`.

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
`n = 30, X = 476.9, s = 42.8`. So

`t = (X - \mu)/((s)/(√(n)))`

`t = (476.9 - 464)/((42.8)/(√(30)))`

`t = 1.65`

The t-value is t = 1.65.