Answer: the t-test statistic is - 1.77
Step-by-step explanation:
For the null hypothesis,
H 0: μ = 2600
For the alternative hypothesis,
H a: μ ≠ 2600
This is a two tailed test
Since no population standard deviation is given, the distribution is a student's t.
Since n = 50,
Degrees of freedom, df = n - 1 = 50 - 1 = 49
t = (x - µ)/(s/√n)
Where
x = sample mean = $2450
µ = population mean = $2600
s = samples standard deviation = $600
Therefore,
t = (2450 - 2600)/(600/√50) = - 1.77