Answer:
The null hypothesis is
The alternate hypothesis is
The pvalue of the test is 0.1515 > 0.01, which means that we do not reject the null hypothesis that 20% of less users develop nausea, that is, we have no sufficient evidence that this proportion is larger than 20%.
Step-by-step explanation:
Test the claim that more than 20% of users develop nausea
This means that the null hypothesis is that 20% or less of the users develop nausea, that is:
And the alternate hypothesis is that more than 20% develop, so:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
0.2 is tested at the null hypothesis:
This means that
Suppose 229 subjects are treated with a drug that is used to treat pain and 52 of them develop nausea.
This means that
Value of the test statistic:
Pvalue of the test an decision:
Probability of finding a proportion above 0.2271, which is 1 subtracted by the pvalue of z = 1.03
Looking at the z-table, z = 1.03 has a pvalue of 0.8485
1 - 0.8485 = 0.1515
The pvalue of the test is 0.1515 > 0.01, which means that we do not reject the null hypothesis that 20% of less users develop nausea, that is, we have no sufficient evidence that this proportion is larger than 20%.