It has been reported in the past that the probability that an individual will develop schizophrenia over their lifetime is 0.004. A researcher believes that this proportion has increased since then. She found out that in a random sample of 2500 individuals, 16 developed schizophrenia.Is there evidence to support the claim that the true proportion of people who will develop schizophrenia is greater 0.004?Use hypothesis testing at α = 0.10 level of significance to answer this question.a. State the null and alternative hypotheses.b. What is the probability model (underlying distribution of the sample proportion \( \hat{p} \))?c. Compute \( \hat{p} \).d. Compute the test statistic.e. Find the P-value.f. Make the decision whether to reject \( H_0 \) or not.g. State a conclusion answering the question above.

The random sample of individuals is 2500The number of individuals with developed schizophrenia is 16.The given claim is that the true population of people who will develop schizophrenia is greater than 0.0004a)Null hypothesis H0:P0 =0.0004The true population of people who will develop schizophrenia is equal to 0.0004Alternate hypothesis H1:P0 >0.0004The true population of people who will develop schizophrenia is greater than 0.0004b.The probability of the model for a given problem is Binomial distribution with size parameter N and probability parameter pc. d.Test statistic:Test statistic for a single proportion ise)p-value:P-value of Z taken from Exel using the function "1-NORM.S.INV(1.90117, TRUE)" for one tail test is 0.02864f)P-value<Z calculated valueReject null hypothesis.g)After comparing Z calculated value and p-value, the conclusion of the given problem is The true population of people who will develop schizophrenia is greater than 0.0004a)Null hypothesis H0:P=0.0004The true population of people who will develop schizophrenia is equal to 0.0004Alternate hypothesis H1:P>0.0004The true population of people who will develop schizophrenia is greater than 0.0004b.The probability of the model for a given problem is Binomial distribution with size parameter N and probability parameter pc)=0.0064d)Test statistic Z=1.90117e)p-value=0.06284f)Reject null hypothesis.g)The true population of people who will develop schizophrenia is greater than 0.0004