Question

A survey was sent out to re-evalute the proportion of people who play games on pc computers, as the last study on the topic had been gathered four years prior. This survey was done specifically to test the possibility that fewer people are playing games on pc computers. The previous study found that 81% of people were playing games on pc computers. The current study, with 861 participants, found that 53% of people who responded play on a pc computer.

Calculate the p-value and determine if we should accept or reject H0 under alpha = 0.05.

Answer 1

`z=\frac{0.53 -0.81}{\sqrt{(0.81(1-0.81))/(861)}}=-20.943`

The p value would be given by:

`p_v =P(z<20.943)\approx 0`

The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81

Explanation:

Info given

n=861 represent the random sample

`\hat p=0.53` estimated proportion of people who responded play on a pc computer

`p_o=0.81` is the value that we want to test

`\alpha=0.05` represent the significance level

z would represent the statistic

`p_v` represent the p value

Hypothesis to test

We want to verify if the true proportion decreases from 81%, the system of hypothesis are.:

Null hypothesis:
`p\geq 0.81`

Alternative hypothesis:
`p < 0.81`

The statistic is given by:

`z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}` (1)

Replacing the info given we got:

`z=\frac{0.53 -0.81}{\sqrt{(0.81(1-0.81))/(861)}}=-20.943`

The p value would be given by:

`p_v =P(z<20.943)\approx 0`

The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81