Question

From a random sample of 87 U.S. adults with no more than a high school education the mean weekly income is $678, with a sample standard deviation of $197. From another random sample of 73 U.S. adults with no more than a bachelor’s degree, the mean weekly income is $1137 with a sample standard deviation of $328 dollars. Construct a 95% confidence interval for the mean difference in weekly income levels between U.S. adults with no more than a high school diplomaand those with no more than a bachelor’s degree. There are 113 degrees of freedom in the appropriate probability distribution.

Technology Results for this problem:

If the problem is a hypothesis test:

1. Give the null and alternative hypotheses; (2 points)

2. Is this a one‐tailed or two‐tailed test? Think about the null hypothesis. How do you know

   that this is a one or two‐tailed test? (1 point)

3. Show whether the criteria for approximate normality are met. (1 point)

4. Summarize the sample statistics (1 point)

5. Give the formula for the test statistic; (1 point)

6. Using the technology results provided, point out the value for the test statistics, degree of

   freedom, and the p-value. (1 point)

7. Using the p-value and the significance level, make a decision on the null hypothesis. (1

   point)

8. What decision can you make about the alternative hypothesis? (1 point)

9. Write your conclusion in the context of the problem. (1 point)

If the problem is a confidence interval:

1. Show whether the criteria for approximate normality are met. (1 point)

2. Summarize the sample statistics. (1 point)

3. Give the formula for the margin of error or test statistic. (1 point)

4. Give the formula for the confidence interval. (1 point)

5. Based on the technology results provided, write the 95% confidence interval. (3 points)

6. Interpret the results in the context of the problem (3 points)

Answer 1

Ans.

Hypothesis:

H0: There is no significant difference btw mean weekly income of people with no bachelor's degree and with bachelor's degree. i.e. Mb=Mh

H1: Mean weekly income of people with no bachelor's degree is greter than people with bachelor's degree. i.e. Mb>Mh

It is a one tailed null hypothesis , since our alternative hypothesis is Mb>Mh .

Test-Statistic:

t=   ~ T(nx+ny-2)

Here Sp = (nx-1)*Sx^2+(n-1)*Sy^2/nx+ny-2 And X: with degree and Y: Without degree.

Sp = 264.857

t = 10.849 ~ T(158)

P-value : P(T>10.849) = 1-P(T<= 10.849) = 1-1 = 0

Since our P-value is less than 0.05 , We have sufficient evidence to reject our null hypothesis at 5% lvl od significance. Hence we can say that the weekly income of people with bachelor's degree is greater than people with no degree or just highschool education.

Now Formulae for 95% confidence Interval is given By:

Margin of error =

Since it is a one tailed test our Conf int will be :

Conf Int : (0,501.308) .