The critical t value for the sample size and significance level given is 2.626 (dof=97, significance level 0.01). To find out what pp is for this critical value involves tricky arithmetic so we’ll use the value 0.04 as the population proportion and see what results. The null hypothesis is that 0.04 is the true proportion.
I worked out the t value by subtracting the population proportion (11/98) from the sample proportion (0.04) and got 0.0722.
Now we need a standard deviation. Let’s assume the variance is 0.04(1-0.04)=0.04×0.96=0.0384, so SD=0.196. Adjusting for the sample size by dividing by √98 we get 0.0198. The t value is 0.0722/0.0198=3.65.
This exceeds the critical number of SDs (2.626) from the mean in a two-tailed test, so the null hypothesis is rejected at the required significance level. We conclude that the population proportion is more likely to differ from 0.04.