Answer:
The claim has no evidence to be supported.
On the contrary, there is enough evidence to support the claim that <em>less than 25% of gamers prefer consoles</em>.
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 <em>less </em>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.
