Question

You think that the average salary of people working in the US is different than $50,000. Write down the null and alternative hypotheses that you want to test. You then collect the salary from a random sample of 10,000 people. The average salary in the sample is $60,000 and the standard deviation is $15,000.

1. Form a 95% confidence interval of the average salary of the population

2. Calculate the Z-Score to test your hypothesis

3. Calculate the p-value for your hypothesis

4. What conclusion can you draw?

5. What if your hypothesis was that the salary is greater than $50,000? Is that supported by the data?

Answer 1

Given:

= $50,000, n = 10,000, = $60,000, Standard deviation (S) = $15,000

Here, sample is larger so we can use Z test.

1) Construct 95% Confidence interval:

Critical value:

Z_/2 = Z _0.05/2 = 1.96

95% Confidence Interval:

(59,706.01, 60,293.99)

We are 95% confident that the population mean is lies in that interval.

2)

Hypothesis:

Or The Average salary of people working in the US is $50,000

Or The average salary of people working in the US is different than $50,000

Test statistic:

3) P-value: 0.00001 .............From standard Normal Table

4) P-value < . i.e. 0.00001 < 0.05, That is Reject Ho at 5% level of significance.

Therefore, The average salary of people working in the US is different than $50,000

5) If our hypothesis was that the salary is greater than $50,000?

Then P-value : 0.00001

Here also,

P-value < . i.e. 0.00001 < 0.05, That is Reject Ho at 5% level of significance.

Therefore, The average salary of people working in the US is greater than $50,000

Yes, This is supported by the data.