03/11/2020 Assignment 5 - Inference for numerical variables
Assignment 5 - Inference for
numerical variables
Click on a question number to see how your answers were marked and, where
available, full solutions.
Question Number Score
Question 1 16 / 18
Question 2 20 / 20
Question 3 24 / 26
Question 4 20 / 20
Total 80 / 84 (95%)
Performance Summary
Exam Name: Assignment 5 - Inference for numerical variables
Session ID: 01165881683
Student's Name: K (Katarina) Djordjevic (011cdd57506642ec949f60ac53aa58da)
Exam Start: Tue Nov 03 2020 19:54:36
Exam Stop: Tue Nov 03 2020 20:20:19
Time Spent: 0:25:43
Question 1
The nutrition label on a bag of potato chips says that a 28 gram serving of potato chips has
187 calories and contains ten grams of fat, with three grams of saturated fat. A random
sample of 49 bags yielded a sample mean of 194 calories with a standard deviation of
14 calories. Is there evidence that the nutrition label underestimates the average number of
calories in the bags of potato chips? The conditions necessary for applying the normal
model have been checked and are satisfied.
https://numbas.up.ac.za/run_attempt/109679?resource_link_id=_2062937_1 1/20
,03/11/2020 Assignment 5 - Inference for numerical variables
a)
What are the correct statistical methods to apply to answer the question?
Inference for the di erence of two means with the normal distribution.
Inference for one-sample mean with the normal distribution.
Inference for a single proportion.
Inference for one-sample mean with the 𝑡 distribution.
Inference for the di erence of two proportions.
Inference for paired data with the normal distribution.
Testing for goodness of fit using chi-square.
Inference for paired data with the 𝑡 distribution.
Inference for the di erence of two means with the 𝑡 distribution.
You chose a correct answer. You were awarded 1 mark.
You scored 1 mark for this part.
Score: 1/1
b)
Complete the following hypothesis statement for the question.
Expected answer: 187.00
𝐻0 : 𝜇 = 187
Expected answer: 187.00
𝐻𝐴 : 𝜇 > 187
Gap 0
Your answer is correct. You were awarded 1 mark.
Gap 1
Your answer is correct You were awarded 1 mark
https://numbas.up.ac.za/run_attempt/109679?resource_link_id=_2062937_1 2/20
, 03/11/2020 Assignment 5 - Inference for numerical variables
Your answer is correct. You were awarded 1 mark.
You scored 2 marks for this part.
Score: 2/2
c)
We wish to calculate the 𝑍 test statistic for the question.
Calculate the Standaard Error (SE) and round your answer to FOUR (4) decimal places.
Expected answer: 2.0000
2.0000
Your answer is correct. You were awarded 2 marks.
You scored 2 marks for this part.
Score: 2/2
d)
Using the calculated Standard Error (SE), calculate the 𝑍 test statistic and round your
answer to TWO (2) decimal places.
Expected answer: 3.50
3.50
Your answer is correct. You were awarded 2 marks.
You scored 2 marks for this part.
Score: 2/2
e)
Use the 𝑍 statistic and find its associated 𝑝-value. Use the normal distribution tables
at the end of the prescribed textbook to determine the answer.
Expected answer: 0.00
0.0002
Your answer is correct. You were awarded 2 marks.
You have not given your answer to the correct precision.
https://numbas.up.ac.za/run_attempt/109679?resource_link_id=_2062937_1 3/20
Assignment 5 - Inference for
numerical variables
Click on a question number to see how your answers were marked and, where
available, full solutions.
Question Number Score
Question 1 16 / 18
Question 2 20 / 20
Question 3 24 / 26
Question 4 20 / 20
Total 80 / 84 (95%)
Performance Summary
Exam Name: Assignment 5 - Inference for numerical variables
Session ID: 01165881683
Student's Name: K (Katarina) Djordjevic (011cdd57506642ec949f60ac53aa58da)
Exam Start: Tue Nov 03 2020 19:54:36
Exam Stop: Tue Nov 03 2020 20:20:19
Time Spent: 0:25:43
Question 1
The nutrition label on a bag of potato chips says that a 28 gram serving of potato chips has
187 calories and contains ten grams of fat, with three grams of saturated fat. A random
sample of 49 bags yielded a sample mean of 194 calories with a standard deviation of
14 calories. Is there evidence that the nutrition label underestimates the average number of
calories in the bags of potato chips? The conditions necessary for applying the normal
model have been checked and are satisfied.
https://numbas.up.ac.za/run_attempt/109679?resource_link_id=_2062937_1 1/20
,03/11/2020 Assignment 5 - Inference for numerical variables
a)
What are the correct statistical methods to apply to answer the question?
Inference for the di erence of two means with the normal distribution.
Inference for one-sample mean with the normal distribution.
Inference for a single proportion.
Inference for one-sample mean with the 𝑡 distribution.
Inference for the di erence of two proportions.
Inference for paired data with the normal distribution.
Testing for goodness of fit using chi-square.
Inference for paired data with the 𝑡 distribution.
Inference for the di erence of two means with the 𝑡 distribution.
You chose a correct answer. You were awarded 1 mark.
You scored 1 mark for this part.
Score: 1/1
b)
Complete the following hypothesis statement for the question.
Expected answer: 187.00
𝐻0 : 𝜇 = 187
Expected answer: 187.00
𝐻𝐴 : 𝜇 > 187
Gap 0
Your answer is correct. You were awarded 1 mark.
Gap 1
Your answer is correct You were awarded 1 mark
https://numbas.up.ac.za/run_attempt/109679?resource_link_id=_2062937_1 2/20
, 03/11/2020 Assignment 5 - Inference for numerical variables
Your answer is correct. You were awarded 1 mark.
You scored 2 marks for this part.
Score: 2/2
c)
We wish to calculate the 𝑍 test statistic for the question.
Calculate the Standaard Error (SE) and round your answer to FOUR (4) decimal places.
Expected answer: 2.0000
2.0000
Your answer is correct. You were awarded 2 marks.
You scored 2 marks for this part.
Score: 2/2
d)
Using the calculated Standard Error (SE), calculate the 𝑍 test statistic and round your
answer to TWO (2) decimal places.
Expected answer: 3.50
3.50
Your answer is correct. You were awarded 2 marks.
You scored 2 marks for this part.
Score: 2/2
e)
Use the 𝑍 statistic and find its associated 𝑝-value. Use the normal distribution tables
at the end of the prescribed textbook to determine the answer.
Expected answer: 0.00
0.0002
Your answer is correct. You were awarded 2 marks.
You have not given your answer to the correct precision.
https://numbas.up.ac.za/run_attempt/109679?resource_link_id=_2062937_1 3/20
