Question

You are required to estimate the proportion of people who are unemployed in South Africa in the first quarter of 2018 at a 99% level of confidence. From a random sample you find 250 are unmployed.

Having observed the trends of unemployment rates over the last 10 years an economist is convinced that the proportion of unemployed South African is far more than 22% of the total population. Is this justified.

1) what type of data is this

2) what assumptions are made

3) using mathematical inequalities to justify the choice of distribution, sketch the distribution, label it, show the critical values, show the test statistic

4) show the formula and all working for the test statistic

Answer 1

1) The data is discrete type, related to the proportion of people who are unemployed in South Africa in the first quarter of 2018.

2) We assume that the number of people who are unemployed in South Africa in the first quarter of 2018 follows binomial distribution which we approximate by normal distribution.

3) The assumption is valid as

Since we are looking for 99% confidence and we have to test whether the proportion of unemployed South African is far more than 22% or not. So from normal table we have the sketch as

The null and the alternative hypothesis are

The value of the test static is given by

Where is the sample size and is the sample proportion.

Here the sample proportion can not be found as sample size is not given.

To do further analysis mention value of