A new provider of ISDN internet access wants to decide whether to commence operations in PG County. It decides to do so only if the proportion of households in PG County that currently do not have high-speed internet access is significantly larger than the nation-wide average. The nation-wide average (for households that do not have high-speed internet access) is known to be 40%.

A survey of 200 randomly selected households in PG County revealed that 96 of them had no high-speed internet access.

A. State the (alternative) research hypotheses that must be proven by the internet provider in order to decide whether to commence operations in PG County.

i.  H_a: The proportion of households in PG County without high-speed internet is less than 48%

ii. H_a: The proportion of households in PG County without high-speed internet is larger than 48%

iii. H_a: The proportion of households in PG County without high-speed internet is different from 40%

iv. H_a: The proportion of households in PG County without high-speed internet is less than 40%

v. H_a: The proportion of households in PG County without high-speed internet is larger than 40%

B. The provider runs the appropriate hypothesis test, and finds that the p-value is 0.0394.At the 5% levelof significance, the internet provider's decision (based on the information only from this test) regarding whether or not to commence operations in PG County is

i.   Reject the Null Hypothesis: Commence operations in PG County

ii.  Do not reject the Null Hypothesis: Do not commence operations in PG County

iii. Reject the Null Hypothesis:  Do not commence operations in PG County

iv. Do not reject the Null Hypothesis: Commence operations in PG County

v.  Inconclusive. Need more information to make decision.

vi. None of the above

C. Insight: Using a 1% level of significance instead of a 5% level of significance would decrease the chances of committing a Type ______________________________________.

i.   Type I error, but increase chances of Type II error

ii.  Type II error, but increase chances of Type I error

iii. Type III error, but increase chances of Type II error

iv. Type II error, but increase chances of Type III error

D. In the context of this problem, committing a Type I error means to

i. Conclude that the proportion of households in PG County without high-speed internet is larger than 40%, when in reality it is the same as the nation-wide average!

ii. Conclude that the proportion of households in PG County without high-speed internet is not larger than 40%, when in reality it is larger than the nation-wide average!

iii. Conclude that the proportion of households in PG County without high-speed internet is larger than 40%, when in reality it is larger than the nation-wide average!

iv. Conclude that the proportion of households in PG County without high-speed internet is not larger than 40%, when in reality it is the same as the nation-wide average!