Question

Colorado economy: the annual business report (1993-1994) indicates that for the past decade the cattle ranching industry in colorado has held steady with a mean total cash receipt of about 2.7 billion dollars annually. a sample of 30 ranches has a mean total cash receipt of 2.85 billion dollars with standard deviation of 0.55 billion dollars. is the colorado cattle ranching expanding?

Answer 1

Answer:

The colorado ranching is not expanding

Explanation:

The null hypothesis, H₀ : μ = 2.7 billion

Alternative hypothesis, Ha : μ > 2.7 billion

$\bar{X} = 2.85 billion$

$\sigma = 0.55 billion$

n = 30

The observed test statistic,

$t_{o} = \frac{\bar{x}- \mu}{\frac{\sigma}{\sqrt{n} } }$

$t_{o} = \frac{2.85- 2.7}{\frac{0.55}{\sqrt{30} } }\\t_{o} = 1.494$

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

$t_{crit} = t_{\alpha, df} = t_{0.05, 29} \\t_{crit} = 1.699$

$t_{0} = 1.494\\t_{crit} = 1.699$

Since$t_{0}$, we will accept H₀

That is the mean total cash receipt is 2.7 billion and the colorado ranching is not expanding