Reference no: EM132349569

In a study a dietician collected a random sample of 2-3 year old children (n=66) in WA population to their dietary intake. The following data set KidsIntake 2019S2QM.dta contains the information with regard to these children's energy, iron and vitamin C intake. The dietician then implemented a small intervention, aiming to improve parents' knowledge on children's nutritional requirements and healthy eating. The parents' knowledge (% statements answered correctly) was measured twice (prior to and after the intervention) in the study. The variables contained in the data set are given as follows in Table 1:

Table 1: Variables in KidsIntake 2019S2QM.dta

The researcher is interested to know if energy intake (ENERGY) and iron intake (IRON) have a Normal distribution. Use the following Table as a guide.

QUESTION 1:

Which of the following would be appropriate?
a. ENERGY and IRON both have a Normal distribution, and hence a natural logarithm transformation is not necessary for both ENERGY and IRON

b. ENERGY and IRON both do not have a Normal distribution, and hence a natural logarithm transformation is necessary for both ENERGY and IRON
c. ENERGY has a Normal distribution and IRON has a right (positively) skewed distribution, and after a natural logarithm transformation, normality can be assumed for the transformed variable ln(IRON)
d. ENERGY has a Normal distribution and IRON has a right (positively) skewed distribution, and after a natural logarithm transformation (ln), normality cannot be assumed for the transformed variable ln(IRON)
e. ENERGY has a Normal distribution and IRON has a left (negatively) skewed distribution, and after a natural logarithm transformation (ln), normality cannot be assumed for the transformed variable ln(IRON)

QUESTION 2: Based on previous question, you now understand whether the variables ENERGY and IRON are normally distributed. What should be the most appropriate measures of centrality and variability to report for variable ENERGY and IRON?
a. Mean and standard deviation for ENERGY. The reason is that variable ENERGY has a normal (symmetric) distribution
b. Mean and standard deviation for IRON. The reason is that variable IRON does not have a normal distribution and it has a skewed distribution
c. Median and interquartile range for IRON. The reason is that variable IRON does not have a normal distribution but a skewed distribution
d. Median and interquartile range for ENERGY. The reason is that variable ENERGY has a normal (symmetric) distribution
e. Answer b) and d) are correct
f. Answer a) and c) are correct

QUESTION 3: Obtain summary statistics for variable ENERGY. Which of the following are NOT CORRECT?
a. The sample mean energy intake of these children is 4764.879 kJ
b. There were 50% of the children, whose energy intake is lower than 4804.95 kJ in this sample

c. There was no any child in this sample whose energy intake higher than 2816.8 kJ
d. The sample standard deviation of energy intake is 850.676 kJ, then we can conclude that 99% of the children in this sample whose energy intake ranged from 3063.528 (i.e., mean-2*SD) to 6466.232 (i.e., mean+2*SD) kJ
e. Both answers c) and d) are not correct

QUESTION 4: Obtain 95% confidence interval for variable ENERGY. Which of the following statement is correct about the estimation of the mean energy intake in the population of the 2 to 3 year old children in WA?
a. Based on the sample information, we are 95% confident that the sample mean daily energy intake of 2 to 3 year old children was between 4555.757 and 4974.001 kJ
b. Based on the sample information, the mean daily energy intake in the population of the 2 to 3 year old children in WA was estimated with 95% certainty to be between 4555.757 and 4974.001 kJ
c. Based on the sample information, there are 95% of the 2 to 3 year old children in WA population having a daily energy intake between 4555.757 and 4974.001 kJ
d. According to the sample information, the average daily energy intake in the population of the 2 to 3 year old children in WA was estimated to be between 4555.757 and 4974.001 kJ
e. Based on the sample information, the mean daily energy intake in the population of the 2 to 3 year old children in WA was estimated with 99% certainty to be between 4555.757 and 4974.001 kJ

QUESTION 5: Which of the following statement related to confidence interval is correct?
a. If the sample size of this study increased from 66 to 660, we will expect the 95% CI to become wider as there is a larger variation now with a larger sample size
b. If the sample size of this study increased from 66 to 660, we will expect the 95% CI to become narrower and be more precise than when the sample size was 66
c. The higher the confidence levels (e.g. from 90% to 95% to 99%), the more confident we are about capturing the actual population parameter and therefore the corresponding lengths of the CIs tend to be shorter
d. The higher the confidence levels (e.g. from 90% to 95% to 99%), the more confident we are about capturing the actual population parameter and therefore the corresponding CIs tend to be wider
e. Answers (a) and (c) are both correct
f. Answers (b) and (d) are both correct

QUESTION 6: The dietician now wants to investigate whether there is an association in energy intake between the children who live in the country and those that live in the city. You need to first recode the variable ENERGY into a categorical variable ENERGYCat according to the following table (Hint: Give the recoded variable a new name and remember to assign value labels to the new recoded variable).

Values of the original variable ENERGY to be recoded into following levels Values of the new recoded variable
ENERGYCat
Less than or equal to 4500 kJ (<= 4500) 1
Greater than 4500 kJ & less than or equal to 5000 kJ (>4500 &<=5000) 2
Greater than 5000 kJ (>5000) 3

Which of the following would be appropriate to describe the frequency distribution of this categorical variable ENERGYCat?
a. Frequency and percentage, and the percentage of kids having energy intake greater than 4500 kJ and less than or equal to 5000 kJ (>4500 &<=5000) is 62.12 % (n=20)
b. Frequency and percentage, and the percentage of kids having energy intake greater than 4500 kJ and less than or equal to 5000 kJ (>4500 &<=5000) is 30.30 % (n=20)
c. Median (=2) and interquartile range (=2)
d. Mean (=2.06) and standard deviation (=0.839)
e. Minimum (=1) and maximum (=3)

QUESTION 7: Based on the new variable you recoded in Question 6, obtain a cross-tabulation of ENERGYCat and LOCATION. Which of the following statements is appropriate to describe the levels of energy intake between the children who live in city and country?
a. More than half of the boys (53.85% of them) lived in city while slightly more of the girls (55.56% of them) lived in city too
b. Of the children who lived in country, more of them tend to have daily energy intake equal or less than 4500 kJ (40.00%), compared to those who lived in city (25.00%)
c. Half (50%) of the country children had daily energy intake between 4500 to 5000 kJ, and the percentage is the same for city children
d. Children who lived in city were more likely to have total daily energy intake >5000 kJ than those kids who lived in country (City 47.22% vs Country 26.67%)
e. Both (b) and (d) are correct

QUESTION 8: Assuming all relevant assumptions are met, how would you test whether there is any association between the levels of energy intake of children ENERGYCat and the location they lived LOCATION?

a. Pearson Correlation Coefficient can be used as ENERGY and LOCATION both are continuous
b. One-way ANOVA is suitable for this research question as LOCATION is continuous and ENERGYCat is categorical with 3 levels

c. An independent (two samples) samples t-test can be used as ENERGY is continuous, and LOCATION is categorical having two levels
d. Chi-square test can be used as ENERGYCat and LOCATION both are categorical
e. Paired samples t-test is fine to answer this research question, as LOCATION and ENERGYCat are repeated variables
1 points

QUESTION 9:  According to the test you chose in Question 8, How can you conclude about the association between levels of energy intake and the location of the children lived (use α =0.05)?
a. The Pearson Correlation Coefficient is 0.2126 with a p value of 0.0865 >0.05. Assuming the assumptions are met, it can be concluded that there is no significant linear relationship between levels of energy intake and location of the children lived
b. The chi-square statistic is 3.1491 with a p-value 0.207 >0.05. Assuming the assumptions are met, it can be concluded that there is no significant association between levels of energy intake and location of the children lived in the population
c. The p-value from the independent (two samples) samples t-test is <0.001. Assuming the assumptions are met, it can be concluded that there is a significant difference in the population mean energy intake between children lived in city and country
d. The p-value from the one-way ANOVA is 0.2144 >0.05. Assuming the assumptions are met, it can be concluded that there is no significant difference in the population mean location among the levels of energy intake
e. The p-value from the Paired samples t-test is <0.001. Assuming the assumptions are met, it can be concluded that there is a significant difference in the population mean energy intake between children lived in city and country

QUESTION 10: The dietician wants to test a research hypothesis that the mean energy intake in this population of the 2-3 years old children μ is equal to 4500 kJ. The correct hypotheses statement(s) for this research objective would be _________. (Hint: this question uses the original continuous variable ENERGY).
a. Ho: μ = 4500 kJ; Ha: μ ≠ 4500 kJ
b. Ho: μ ≠ 4500 kJ; Ha: μ = 4500 kJ
c. Null hypothesis: the sample mean energy intake of the 2-3 years old children is 4500 kJ; Alternate hypothesis: the sample mean energy intake of the 2-3 years old children is not 4500 kJ
d. Null hypothesis: the mean energy intake in this population of the 2-3 years old children is equal to 4500 kJ; Alternate hypothesis: the mean energy intake in this population of the 2-3 years old children is not equal to 4500 kJ
e. Statements (a) and (d) are both correct

QUESTION 11: Assume 5% level of significance (α =0.05). The appropriate statistical test to test that hypothesis in Question 10 would be __________ ; and the results are found to be ________
a. One sample t-test; t-value = 2.5296, p-value = 0.0139
b. Two samples (independent samples) t-test; t-value = 3.84, p-value = <0.001
c. Paired-sample t-test; t-value = 0.64, p-value = 0.527
d. One-way ANOVA; t-value = -5.57, p-value = <0.001
e. Pearson correlation coefficient; r = 0.08, p-value = 0.520

QUESTION 12: An appropriate conclusion about the research hypothesis (in Question 10) would therefore be ________
a. The population mean energy intake of the 2-3 years old children is equal to the test value, 4500 kJ, as the p-value is close to zero, means no difference
b. Because the sample mean energy intake is 4764.879kJ, which is higher than the hypothesized 4500 kJ, and therefore the alternative hypothesis has to be rejected
c. The p values of the one sample t-test 0.0139 is less than 0.05, in addition, the estimated 95% confidence interval of the population mean energy intake (4555.757, 4974.001) does not include the hypothetical value '4500', hence the null hypothesis has to be rejected at 5% significance level. We conclude that the population mean energy intake of the 2-3 years old children is significantly different to 4500 kJ

d. The p-value the one sample t-test is not much different from 0.05. In addition, the 95% confidence interval of the population mean does not include the hypothetical value ‘4500', therefore supporting the decision to accept the null hypothesis and conclude that the population mean energy intake of the 2-3 years old children is equal to 4500 kJ
e. Both answers b) and c) are correct

QUESTION 13: The dietician now wishes to test the hypothesis that the population mean energy intake µ is the same for the boys and girls. You will test the hypothesis by following the steps of hypothesis testing. The appropriate null and alternative hypothesis will be_____________. (Hint: this question uses the original continuous variable ENERGY).

a. H0: the sample mean energy intake is the same for the boys and girls, HA: the sample mean energy intake is different for the boys and girls
b. H0: the energy intake is the same for the boys and girls, HA: the energy intake is different for the boys and girls
c. H0: µboys ≠ µgirls, HA: µboys = µgirls
d. H0: µboys - µgirls = 0, HA: µboys - µgirls ≠ 0
e. Both a) and d)

QUESTION 14: Assume 5% level of significance (α =0.05), state which statistical test you plan to use to test the hypotheses stated above in Question 13 .
a. One sample t-test
b. Paired samples t-test
c. Independent samples (two-samples) t-test
d. One-way ANOVA
e. Chi-square test

QUESTION 15: Which of the followings are assumptions for the statistical test you nominated in Question 14?
a. Random sampling and independent observations
b. The cells are mutually exclusive and exhaustive, and no more than 20% of the expected frequencies are less than 5
c. Normality of the variable of interest (energy intake: ENERGY), and equal variances between the 2 gender groups
d. Both (a) and (c)
e. Both (a) and (b)

QUESTION 16: After evaluated the relevant assumptions associated with the test you nominated in Question 15. Which of the following statements is correct? (Hint: you have assessed the normality of ENERGY in Question 1).

a. Normality can be assumed for ENERGY. However the assumption of equal variances is not met, hence I will use the original ENERGY to do the t-test with unequal variances
b. Normality can be assumed for ENERGY and the assumption of equal variances is met too and I will use the original ENERGY to do the t-test with equal variances
c. Normality cannot be assumed for ENERGY and a natural logarithm transformation is applied to ENERGY. The assumption of equal variances is not met and I will use the original ENERGY directly to do the t-test with unequal variances
d. Normality cannot be assumed for ENERGY and a natural logarithm transformation is applied to ENERGY. The assumption of equal variances is met after transformation and I will use the transformed ENERGY to do the t-test with equal variances
e. None of the above as the test does not need to assess the normality and equal variances

QUESTION 17: After you run the statistical test for the research hypotheses stated in Question 16, what can you conclude about it?
a. The test statistics is 45.4916, the p-value is <0.001, the 95% CI of the difference is (4556.312, 4970.628) and does not include ‘0', suggesting that we have to reject the null hypothesis and conclude that the population mean energy intake is significantly different between the boys and the girls
b. The test statistics is 2.2638, the p-value is 0.0270, the 95% CI of the difference is (54.939, 880.082) and does not include ‘0', suggesting that we have to reject the null hypothesis and conclude that the population mean energy intake is significantly different between the boys and the girls
c. The test statistics is 2.1832, the p-value is 0.0339, the 95% CI of the difference is (37.092 897.929) and does not include ‘0', suggesting that we have to reject the null hypothesis and conclude that the population mean energy intake is significantly different between the boys and the girls
d. The test statistics is 2.3804, the p-value is 0.0203, the 95% CI of the difference is (0.018, 0.201) and does not include ‘0', suggesting that we have to accept the null hypothesis and conclude that the population mean energy intake is the same between the boys and the girls
e. Answers a), b) and c) are all correct as they all reject the null hypothesis

QUESTION 18: The dietician then wants to know whether the population mean parents' knowledge on children's nutritional requirements and healthy eating after the intervention are the same as their knowledge before the intervention. The appropriate null and alternative hypothesis will be, assuming µ is the population mean parents' knowledge.
a. H0: µafter = µbefore, HA: µafter ≠ µbefore
b. H0: µbefore = µafter, HA: µbefore ≠ µafter
c. H0: µbefore - µafter = 0, HA: µbefore - µafter ≠ 0
d. H0: µafter - µbefore = 0, HA: µafter - µbefore ≠ 0
e. All the above are correct

QUESTION 19: To test the hypothesis stated in Question 18 (α= 0.05), the appropriate hypothesis test would be____________.
a. One sample t-test
b. Paired samples t-test
c. Independent samples (two-samples) t-test
d. One-way ANOVA
e. Chi-square test

QUESTION 20: Assuming the assumptions for the statistical test you chose to do above are met, what can you conclude about the research hypothesis after you run the statistical test (Assume 5% level of significance: α =0.05)?
a. The mean difference between the parents' knowledge on children's nutritional requirements and healthy eating after and before the intervention is 1.806 units. The t-value is 2.8323, p-value is 0.0061, 95% CI of the difference is (0.532, 3.079) units and does not include ‘0', suggesting that there is a significant difference in the population mean parents' knowledge on children's nutritional requirements and healthy eating between after and before the intervention, with the parents' knowledge after the intervention higher by 1.806 units on average in the population
b. The mean difference between the parents' knowledge on children's nutritional requirements and healthy eating before and after the intervention is -1.806 units. The t-value is -2.8323, p-value is 0.0061, 95% CI of the difference is (-3.079, -0.532) units and does not include ‘0', suggesting that there is a significant difference in the population mean parents' knowledge on children's nutritional requirements and healthy eating between before and after the intervention, with the parents' knowledge before the intervention lower by 1.806 units on average in the population
c. It is found that the Pearson's r value is 0.678, the p-value is <0.0001, we hence reject the null hypothesis and conclude that suggesting that the parents' knowledge on children's nutritional requirements and healthy eating after the intervention is 0.678 unit higher than the parents' knowledge before the intervention
d. Only statement (c) is incorrect

QUESTION 21: Furthermore the dietician wishes to test whether the parents' knowledge on children's nutritional requirements and healthy eating before the intervention KNOW1 varies significantly across the 3 energy levels of their children consumed at the population level. Using the categorical variable ENERGYCat (Hint: you have obtained this variable in Question 6) and assuming 5% level of significance, the appropriate test to use would be?
a. Two samples (independent samples) t-test
b. Paired-sample t-test
c. One-way ANOVA
d. Chi-square test
e. Pearson's correlation

QUESTION 22: What can you conclude about the research hypothesis in Question 21?
a. The t-statistic is 93.0784, p-value is <0.001, the 95% CI of the difference is (56.400, 58.850) kJ and does not include ‘0', suggesting that in this population, there is a significant difference between the parents' knowledge on children's nutritional requirements and healthy eating before the intervention and children's daily energy intake in the population
b. The t-statistic is 91.1044, p-value is <0.001, the 95% CI is (56.362, 58.889) kJ and does not include ‘0', suggesting that in this population, there is a significant difference between the parents' knowledge on children's nutritional requirements and healthy eating before the intervention and children's daily energy intake in the population
c. The Pearson's correlation coefficient r is -0.1332, p-value is 0.2865, suggesting that there is no strong variation between the parents' knowledge on children's nutritional requirements and healthy eating before the intervention and children's daily energy intake in the population
d. The χ2 statistic is 60.8740, p-value is 0.030, suggesting that there is a significant difference between the parents' knowledge on children's nutritional requirements and healthy eating before the intervention and children's daily energy intake in the population
e. The F test-statistic is 0.58, p-value is 0.5602, suggesting that there are no significant difference in the population mean parents' knowledge on children's nutritional requirements and healthy eating before the intervention across the groups of children who had different levels of energy intake

QUESTION 23: Lastly, the dietician wants to know whether, at population level, the parents' knowledge on children's nutritional requirements and healthy eating after the intervention can be predicted by the parents' knowledge before the intervention. You can assume that the assumptions for the statistical approach you chose to partake are met. Which of the following is the appropriate statistical analysis?

a. Scatter plot using KNOW1 as Y variable and KNOW2 as X variable; Paired samples t-test; and simple linear regression using KNOW1 as a dependent variable and KNOW2 as an independent variable
b. Scatter plot using KNOW2 as Y variable and KNOW1 as X variable; Pearson's correlation coefficient; and simple linear regression using KNOW2 as a dependent variable and KNOW1 as an independent variable
c. Scatter plot using KNOW2 as Y variable and KNOW1 as X variable; Pearson's correlation coefficient; and simple linear regression using KNOW1 as a dependent variable and KNOW2 as an independent variable
d. Scatter plot using KNOW2 as Y variable and KNOW1 as X variable; Chi-square test; and multiple linear regression using KNOW2 as a dependent variable and KNOW1 as an independent variable
e. Both answers b) and c) are correct

QUESTION 24: Based on the analyses you conducted in previous question, which of the following are the correct conclusion?
a. Predicted equation is given as: predicted KNOW2 = 4.028 + 0.963* KNOW1, and R2 value is 0.4597, indicating there were approximately 46% of parents, whose knowledge (i.e., KNOW1) improved after the intervention in KNOW2
b. Predicted equation is given as: predicted KNOW1 = 4.028 + 0.963* KNOW2, and R2 value is 0.4597, indicating KNOW1 only explains approximately 46% of variation in KNOW2
c. Predicted equation is given as: predicted KNOW2 = 4.028 + 0.963* KNOW1, and R2 value is 0.4597, indicating KNOW1 only explains approximately 46% of variation in KNOW2
d. Predicted equation is given as: predicted KNOW1 = 30.326 + 0.477* KNOW2, and R2 value is 0.4597, indicating KNOW2 only explains approximately 46% of variation in KNOW1
e. Predicted equation is given as: predicted KNOW1 = 30.326 + 0.477* KNOW2, and R2 value is 0.4597, indicating there were approximately 46% of parents, whose knowledge (i.e., KNOW1) improved after the intervention in KNOW2
f. Predicted equation is given as: predicted KNOW2 = 30.326 + 0.477* KNOW1, and R2 value is 0.4597, indicating KNOW1 only explains approximately 46% of variation in KNOW2

QUESTION 25: Based on the analyses you conducted, which of the following are the correct conclusion?
a. The Pearson's correlation coefficient (0.6780) indicates that there is a strong positive linear and also significant (p<0.001) relationship between the parents' knowledge on children's nutritional requirements and healthy eating before and after the intervention, suggesting those parents with higher knowledge on children's nutritional requirements and healthy eating before the intervention tend to have improved knowledge after the intervention
b. The Pearson's correlation coefficient (0.6780) indicates that there is a strong negative linear and also significant (p<0.001) relationship between the parents' knowledge on children's nutritional requirements and healthy eating before and after the intervention, suggesting higher knowledge values after the intervention are associated with lower knowledge before the intervention
c. For each one unit of score increased in the parents' knowledge on children's nutritional requirements and healthy eating before the intervention, the parents' knowledge after the intervention is increased by 0.963 units on average, with 95% certainty the parents' knowledge is increased by between 0.702 and 1.223 units on average in the population after the intervention
d. For each one unit of score increased in the parents' knowledge on children's nutritional requirements and healthy eating after the intervention, the parents' knowledge before the intervention is increased by 0.477 units on average, with 95% certainty the population mean parents' knowledge is increased by between 0.348 and 0.607 units before the intervention
e. Answers (a) and (c) are correct
f. Answers (b) and (d) are correct

QUESTION 26: Please make sure you have answered all the above 25 questions in this quiz!
Before you hit the 'Save and Submit' button, you need to provide outputs you generated from STATA as evidence to support your given answers. The outputs for Questions 1, 3, 4, 6, 7, 9, 11, 17, 20, 22, and 24 should be provided on a word document and uploaded here by clicking Browse My Computer tab.