Question

a poll taken by the software usability research laboratory surveyed 341 video gamers, and 126 of them said that they prefer playing games on a console, rather than a computer or hand-held device. an executive at a game console manufacturing company claims that more than 30% of gamers prefer consoles. does the poll provide convincing evidence that the claim is true?

Answer 1

The poll shows that approximately 36.95% of video gamers surveyed prefer consoles, which supports the executive's claim that more than 30% of gamers prefer consoles. However, for conclusive evidence, we should perform a hypothesis test and analyze the margin of error and confidence interval, which requires additional information not provided in the poll.

Step-by-step explanation:

A poll conducted by the software usability research laboratory surveyed 341 video gamers, and 126 of them expressed a preference for playing games on a console. To assess whether this poll provides convincing evidence that more than 30% of gamers prefer consoles, we can perform a hypothesis test using the sample proportion.

First, we calculate the sample proportion of gamers who prefer consoles:

• Sample Proportion (p) = Number preferring consoles / Total surveyed = 126/341 = 0.3695 (36.95%)

This initial calculation shows that, in the sample, around 36.95% of gamers prefer console gaming, which is indeed more than the 30% claimed by the executive. However, to determine if this is convincing evidence for the population of gamers, we must consider the margin of error and confidence interval. Without additional information such as the desired level of confidence or the standard deviation, we cannot calculate the confidence interval. However, since the sample proportion is higher than 30%, the executive's claim is supported by the poll.

It's important to note that to make a more definitive statement about the gaming preferences of the entire population of gamers, we would conduct a hypothetical test such as a one-proportion z-test. Additionally, we would need to ensure our sample is representative, randomly selected, and sufficiently large to infer population preferences. Also, regardless of the poll results, there could always be a margin of error due to sampling variability.

Considering all these points, the provided information does support the executive's claim to a certain extent. Conclusive evidence would require further statistical analysis.