1. At the national level, the average income for a given occupation is $74 914. You want to determine if the income for member of the occupation is the same in Chicago. You take a random sample of 112 members of the occupation in Chicago. You find that mean of your sample is $78 695. Assume that the population standard deviation is $14 530.

Question

1. At the national level, the average income for a given occupation is $74 914. You want to determine if the income for member of the occupation is the same in Chicago. You take a random sample of 112 members of the occupation in Chicago. You find that mean of your sample is $78 695. Assume that the population standard deviation is $14 530.
(a) State the hypotheses and test them with the critical value approach and a
significance level of α = 0.05.
(b)What is the p-value of the test statistic?
(c)What is the 95% confidence interval for μ?

2. Consider the following data:
23 17 20 29 21 14 19 24
Develop and test a hypothesis to determine if the variance is greater than 4

I am very confused on these two questions, please help somehow

PsyDAG · Answer

Here is a beginning:

1. Z = (score-mean)/SD = (78695-74914)/14530

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability of that Z score.

2. Find the mean first = sum of scores/number of scores

Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.