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

The colorado ranching is not expanding

Step-by-step 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}{(\sigma)/(√(n) ) }`

`t_(o) = (2.85- 2.7)/((0.55)/(√(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) <t_(crit)`, we will accept H₀

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