Both the P-value method and the critical value method use the same standard deviation based on the claimed proportion p, so they are equivalent to each other. Is this also true about the confidence interval method?

Yes, it's also true about the confidence interval method.

Step-by-step explanation:

The confidence interval includes all the null hypothesis values for the population mean that would be accepted by the hypothesis test at the significance level of 5%. Now, it means this assumes a two-sided alternative.

Now, when testing claims about

population proportions, the critical method and the P-value method are equivalent due to the fact that they always produce the same result. Similarly, a conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

So, Yes the confidence interval method and the P-value or critical methods will always lead to the same conclusion when the tested parameter is the standard deviation.

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.

what i would say the best answer is a. 40.5