Question

Sully, the best scarer of the company Monsters Inc, assures that most of the children have stopped being scared by monsters and he is worried that soon they will no longer have the energy to supply the city of Monstruopolis.

To demonstrate this, he obtained a sample of 41 children from the paperwork that Mike Wasowsky carried out and obtained that 25 of them were not scared.

a) With this result, can Sully conclude that more than 50% of children are no longer scared of monsters? Perform a hypothesis test using a significance level of 0.1 to conclude.

b) Calculate the p-value and conclude within the problem using this using this value.

c) If Sully wants the difference between the actual proportion and the estimated proportion of children who are not frightened to be more than 0.05 with a confidence level of 96%, what size should the sample select?

Answer 1

a. Here claim is that p>0.50

As null hypothesis is always having equality sign, so hypothesis here is vs

Now

So the test statistics is

The z-critical value for a right-tailed test, for a significance level of α=0.1 is

zc​=1.28

Graphically

As test statistics fall in the rejection region, we reject the null hypothesis

b. P value is

We reject the null hypothesis, hence we have sufficient evidence to support the claim that p>0.5

c. z value for 96% CI is 2.054 as P(-2.054<z<2.054)=0.96

Margin of Error=E=0.05 and p=0.61

So we will find n, using formula of E

So