many gamers have reported experiencing motion sickness from using virtual reality (vr) glasses. a new brand…

many gamers have reported experiencing motion sickness from using virtual reality (vr) glasses. a new brand of vr glasses is more expensive, but the makers claim the new brand is less likely to make users motion sick. the makers say that the proportion of gamers who will experience motion sickness from using their glasses is 25% or less. you work for the leading competitor and are doubtful of the claim. to test it, you decide to perform a hypothesis test. to do so, you choose 175 gamers at random and have each of them use the glasses. of these gamers, 49 said that using the glasses made them motion sick. you confirm that it is appropriate to perform a z - test. why is a z - test appropriate? find z, the value of the test statistic for your z - test. round your answer to three or more decimal places. z =

many gamers have reported experiencing motion sickness from using virtual reality (vr) glasses. a new brand of vr glasses is more expensive, but the makers claim the new brand is less likely to make users motion sick. the makers say that the proportion of gamers who will experience motion sickness from using their glasses is 25% or less. you work for the leading competitor and are doubtful of the claim. to test it, you decide to perform a hypothesis test. to do so, you choose 175 gamers at random and have each of them use the glasses. of these gamers, 49 said that using the glasses made them motion sick. you confirm that it is appropriate to perform a z - test. why is a z - test appropriate? find z, the value of the test statistic for your z - test. round your answer to three or more decimal places. z =

Answer

Explanation:

Step1: Calculate sample proportion

The sample size $n = 175$ and the number of gamers who experienced motion - sickness $x = 49$. The sample proportion $\hat{p}=\frac{x}{n}=\frac{49}{175}=0.28$.

Step2: Identify hypothesized proportion

The hypothesized proportion $p_0 = 0.25$.

Step3: Calculate the standard error

The formula for the standard error of a proportion in a one - sample z - test is $SE=\sqrt{\frac{p_0(1 - p_0)}{n}}$. Substituting $p_0 = 0.25$ and $n = 175$, we get $SE=\sqrt{\frac{0.25\times(1 - 0.25)}{175}}=\sqrt{\frac{0.25\times0.75}{175}}=\sqrt{\frac{0.1875}{175}}\approx\sqrt{0.00107143}\approx0.0327$.

Step4: Calculate the z - statistic

The formula for the z - statistic in a one - sample proportion test is $z=\frac{\hat{p}-p_0}{SE}$. Substituting $\hat{p}=0.28$, $p_0 = 0.25$ and $SE\approx0.0327$, we get $z=\frac{0.28 - 0.25}{0.0327}=\frac{0.03}{0.0327}\approx0.917$.

Answer:

$0.917$