Question

Question 5: It is known that the socioeconomic status (SES) of each family follows a normal distribution. The SES data of 16 families shows blow using a stem leaf plot. The SES survey score could go from 0 to 100.

  0 | 9

  1 | 49

  2 | 37

  3 | 01449

  4 | 19

  5 | 23

  6 | 2

  7 | 1

1. Calculate the 95% CI to estimate the average SES score of the population.

2. Interpret the 95% CI.

3. Question 6: It is known that the population wellbeing score follows a normal distribution with the mean of 30 and the SD of 7. A researcher hypothesizes that the college students have a different Wellbeing level from the population average, so the researcher randomly selected 49 students and found the average well being score of them is 32. The significant hypothesis test at 0.05 level is shown below.

Identify and correct the mistakes in the test below:

Step 1:

Null hypothesis: The college students have a different wellbeing level from the population

Alternative hypothesis: The college students have a higher wellbeing level than the population

Step 2: =0.05, two tailed, Critical z= 1.65

Step 3:

Obtained Z=x-SE =32-30749 = 2

Step 4: conclusion

Since the obtained z = 2 is more extreme than the critical z = 1.65, we fail to reject the null hypothesis. We infer that college students have a higher wellbeing level from the population.

Question 7: It is known that the population wellbeing score follows a normal distribution with a mean of 30. A researcher hypothesizes that the college students have a higher Wellbeing level than the population average, so the researcher randomly selected nine students and listed their wellbeing score below. Conduct a hypothesis test to test the hypothesis at the 0.05 level.     

   | 9

1 | 5

2 | 79

3 | 14456

4 | 2

Answer 1

QUESTION 6

STEP 1 ALTERNATIVE HYPOTHESIS : THE COLLEGE STUDENTS DOES NOT HAVE DIFFERENT WELLBEING LEVEL FROM THE POPULATION

STEP 2 : CRITICAL VALUE Z =1.96

STEP 3 : FORMULA (X-U)\(S\ROOT N)

STEP 4 : WE WRITE WE HAVE SUFFICIENT EVIDENCE TO ACCEPT NULL HYPOTHESIS.