Question

A popular podcast wants to know the proportion of listeners that think assault weapons should be banned for civilians. Listeners are asked to text "Y" for yes or "N" for no to a provided number. Sixty-five percent of the 1,500 people that responded texted "Y." Which condition for inference has NOT been met?A) All conditions appear to be met.B) The sample is an SRS of the population.C) N > 10nD) np ≥ 10 and n(1 - p) ≥ 10E) Inference about a proportion is the objective.

Answer 1

The condition for inference that is not met is that the sample is not a Simple Random Sample (SRS) of the population because the method of selection is not described and may introduce bias if it is self-selected.

Step-by-step explanation:

The condition for inference that has NOT been met is B) The sample is an SRS of the population. In this context, an SRS stands for Simple Random Sample, which means every member of the population has an equal chance of being selected for the sample. Since the question doesn't provide details on how the samples were chosen, it cannot be assumed that an SRS was employed. Instead, if respondents are self-selected, such as those who are motivated to respond to a podcast's call to text, this could introduce bias and does not represent an SRS. Therefore, one cannot confidently infer that the sample proportion of 65% who responded 'Y' reflects the view of the entire listener population.

Answer 2

The inference condition that has NOT been met is B) The sample is an SRS of the population because the podcast's voluntary response method does not ensure a random or representative sample.

Step-by-step explanation:

To determine which condition for inference has NOT been met in a situation where a popular podcast asks its listeners to text "Y" for yes or "N" for no on banning assault weapons, we review each condition against the scenario provided:

• SRS (Simple Random Sample) - It is not clear whether the sample of listeners who responded is an SRS of all listeners. The podcast seems to have used a voluntary response sampling method, which is not random or representative.
• N > 10n - This condition is related to finite population correction factor, used when sample size is a significant fraction of the population. Here, it's unlikely that 1,500 is a large fraction of the population of all podcast listeners.
• np ≥ 10 and n(1 - p) ≥ 10 - With 65% of 1,500 respondents saying "Y", this condition is met because both np = 975 and n(1 - p) = 525 are greater than 10.
• Inference about a proportion - This condition aims for inferring a population proportion, which the podcast is attempting to estimate.

Therefore, the condition that has NOT been met is B) The sample is an SRS of the population, as the sampling method used does not guarantee randomness or representativeness.