Step 1 :State the null hypothesis and the alternative hypothesis. The null hypothesis is \(H_{0}: p=0.20\) and the alternative hypothesis is \(H_{1}: p>0.20\).
Step 2 :The test statistic for this hypothesis test is 1.82.
Step 3 :Use the test statistic to find the P-value. The P-value is the probability that we would observe a test statistic as extreme as the one we have, or more extreme, if the null hypothesis were true.
Step 4 :Since we are testing the claim that more than 20% of users develop nausea, we are looking for the probability that we would observe a test statistic of 1.82 or greater, given that the true proportion is 20%.
Step 5 :This is a one-tailed test, so we will use the cumulative distribution function (CDF) of the standard normal distribution to find the P-value. The CDF gives the probability that a random variable drawn from the given distribution is less than or equal to a given value, so to find the P-value, we need to subtract the value of the CDF at the test statistic from 1.
Step 6 :The P-value for this hypothesis test is 0.034.
Step 7 :Final Answer: The P-value for this hypothesis test is \(\boxed{0.034}\).