Answer to Question #169284 in Statistics and Probability for Suzeth

Question

For the United States, the mean monthly Internet bill is $32.79 per household (CNBC, January 18, 2006). A sample of 50 households in a southern state showed a sample mean of $30.63. Use a population standard deviation of $5.60. Formulate hypothesis for a test to determine whether the sample data support the conclusion that the mean monthly internet bill in the southern state is less than the national mean $32.79.

Answer 1

$n = 50 \\ \bar{x} = 30.63 \\ σ = 5.60 \\ α = 0.01 \\ H_0: \; μ ≥ 32.79 \\ H_1: \; μ< 32.79 \\ Z = \frac{\bar{x}-μ}{σ/ \sqrt{n}} = \frac{30.63-32.79}{5.60/ \sqrt{50}} = -2.73 \\ P = P(Z<-2.73) = 0.0032 \\ P < 0.01 \\ Reject \; H_0.$