Answer:
The colorado ranching is not expanding
Explanation:
The null hypothesis, H₀ : μ = 2.7 billion
Alternative hypothesis, Ha : μ > 2.7 billion
[tex]\bar{X} = 2.85 billion[/tex]
[tex]\sigma = 0.55 billion[/tex]
n = 30
The observed test statistic,
[tex]t_{o} = \frac{\bar{x}- \mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
[tex]t_{o} = \frac{2.85- 2.7}{\frac{0.55}{\sqrt{30} } }\\t_{o} = 1.494[/tex]
Degree of freedom = n-1 = 30 -1 = 29
Significance level = 0.05
For the critical value, we check the t - table at 0.05 significance level
[tex]t_{crit} = t_{\alpha, df} = t_{0.05, 29} \\t_{crit} = 1.699[/tex]
[tex]t_{0} = 1.494\\t_{crit} = 1.699[/tex]
Since[tex]t_{0} <t_{crit}[/tex], we will accept H₀
That is the mean total cash receipt is 2.7 billion and the colorado ranching is not expanding
