Question

Formulate the Null and alternative hypothesis, identify the level of significance, illustrate if CLT Can be Used and illustrate the rejection region.

Teacher Sara reported that out of her 300 students, 84% prefer to be contacted through online messaging. test the hypothesis with 95% level of confidence.​

Answer 1

Answer:

Hypothesis Testing using the Central Limit Theorem

Using the Central Limit Theorem we can extend the approach employed in Single Sample Hypothesis Testing for normally distributed populations to those that are not normally distributed. Suppose we take a sample of size n, where n is sufficiently large, and pose a null hypothesis that the population mean is the same as the sample mean; il

If we assume the null hypothesis, we know from the Central Limit Theorem that the sample mean has a normal distribution

This approach works well provided the variance of the population is known, which is not so common.

As we saw in Property 3 of Estimators, the variance of the sample is an unbiased estimator of the variance of the population, and so when the variance of the population is not known, we can estimate σ2 by s2.

As was done in Confidence Intervals for Sampling Distributions we can now set a confidence interval for the population mean