A poll surveyed 503 video gamers, and 106 of them said they prefer playing games on a console rather than a computer. An executive at a game console company claims that more than 25% of gamers prefer consoles. Does the poll provide convincing evidence that the claim is true? Use the level of significance.

The claim has no evidence to be supported.

On the contrary, there is enough evidence to support the claim that less than 25% of gamers prefer consoles.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The sample has a size n=503.

The sample proportion is p=0.211.

p=X/n=106/503=0.211

The sample proportion is less than 25%, so we will test the claim that less than 25% of gamers prefer consoles.  

Then, the null and alternative hypothesis are:

The significance level is assumed to be 0.05.

The standard error of the proportion is:

Then, we can calculate the z-statistic as:

This test is a left-tailed test, so the P-value for this test is calculated as:

As the P-value (0.0245) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that less than 25% of gamers prefer consoles.

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