QUESTION 3

Suppose you are interested in whether participation in extracurricular activity is associated with higher academic achievement. In a sample of 250 students who participated in 2 or more extracurricular activity 147 kids were high achievers (scored 80% or more on the Standardized test) while among 350 students who did not report to participate in any extracurricular activity 168 were high achievers.

Which of the following are the most appropriate null and alternative hypotheses?

A H0: There is an association between participation in extracurricular activities and high scores (80% or more) in standardized testing.

HA: There is no association between participation in extracurricular activities and high scores (80% or more) in standardized testing.

B H0: The proportion of high achievers in the extracurricular group is less than or equal to the proportion of high achieves in the non-extracurricular group.

HA: The proportion of high achievers in the extracurricular group is greater than the proportion of high achieves in the non-extracurricular group.

C H0: The proportion of high achievers in the extracurricular group is equal to the proportion of high achieves in the non-extracurricular group.

HA: The proportion of high achievers in the extracurricular group is not equal to the proportion of high achieves in the non-extracurricular group.

D H0: The proportion of high achievers in the extracurricular group is equal to the proportion of high achieves in the non-extracurricular group.

HA: The proportion of high achievers in the extracurricular group is greater than the proportion of high achieves in the non-extracurricular group.

[2 marks]

QUESTION 8

A parallel-group randomised control trial of a new infertility treatment is being trialled. Women undergoing treatment for infertility were invited to participate and were randomised in a 1:1 ratio to receive either the standard treatment or the intervention (PICSI).

The primary outcome is term live-birth ( = 37 weeks gestational age) within the study follow-up period of 2 years.

The expected term live-birth rate is 24% using the standard treatment. The study aims to detect a 5% increase (from 24% to 29%) in the term live-birth rate in the PICSI treatment group with power 90% and alpha 5%, allowing for a 10% drop-out rate.

Calculate the minimum total recruitment target that will sufficiently power the study.

Note: the numbers below indicate targets that have been rounded up to the nearest 50. Select the best option based on to your Stata/PSPower calculation.

A 1650

B 2750

C 3300

D 3650

QUESTION 9

If the observed difference between groups is larger than expected (i.e. greater than 5%), will the recruitment target still provide the analysis with sufficient power?

QUESTION 10

Burr et al. (1976) tested a new procedure to remove house-dust mites from the bedding of adult asthmatics in attempt to improve subjects' lung function, which was measured by PEFR (peak expiratory flow rate). The trial was a two period cross-over design; the control treatment was dust removal from the living room. The means and standard errors for the continuous variable PEFR in the 32 subjects were:

Treatment group Mean Standard Error

Control 329 litres/min 20.8 litres/min

New procedure 335 litres/min 19.6 litres/min

Differences (Treatment - Control) 6.45 litres/min 5.05 litres/min

The researchers decide to perform a one sample t-test on the differences with a significance level of 5%. Which of the following options is correct?

A The test statistic is 1.3 and the associated p-value is statistically significant.

B The test statistic is 1.3 and the associated p-value is not statistically significant.

C The test statistic is 7.2 and the associated p-value is statistically significant.

D There’s not enough information.

QUESTION 11

A cohort of students of a certain age underwent standardised tests in Maths and English. The top 2.5% of students in each subject were awarded medals.

The scores on the Maths test were normally distributed with mean 55 and standard deviation 10. The scores on the English test were normally distributed with mean 60 and standard deviation 13.

Chloe’s marks were 77 in Maths and 85 in English. Will she receive any medals?

A Chloe will receive a medal for English

B Chloe will receive a medal for Maths

C Chloe will receive a medal for Maths and a medal for English

D Chloe will not receive any medals.

QUESTION 12

The Apgar test is used to evaluate the health of a newborn at 1 minute and 5 minutes after birth. Each of five items is scored between 0 and 2. A total score between 7 and 10 is considered normal, a total score between 4 and 6 indicates the infant requires medical attention, and a total score between 0 and 3 indicates the infant requires immediate resuscitation.

The distribution of Apgar scores of a sample of 100 babies with low birth weight has descriptive summary:

n mean sd min p25 median p75 max

100 6.25 2.43 0 5 7 8 9

Which of the following is NOT true?

A The interquartile range is 3

B The distribution is symmetric

C The range is 9

D There were no infants with a score of 10

QUESTION 13

Brown et. al., Morbidity and mortality in patients randomised to double-blind treatment with a long-acting calcium-channel blocker or diuretic in the INSIGHT study, Lancet 356, 29 July 2000.

Which of the following best describes the type of primary outcome?

A) Continuous

B) Categorical

C) Binary

D) Count

QUESTION 14

A group of 11 patients were recruited for a new weight loss diet regimen. Patients were weighed at baseline before the start of a new diet regimen. At the end of 6 weeks patients were weighed again. The mean and variance of the change in weight after 6 weeks were 0.7 and 1.44. Assume that the change in weight is normally distributed. Researchers are interested in whether there was a significant change in weight from baseline to 6 week followup.

What is the most appropriate hypothesis test for the above scenario?

a) Two sample independent t-test

b) Wilcoxon ranked sum test

c) Chi-squared test

d) One sample t-test

QUESTION 16

If a statistical test fails to show a statistically significant test statistic, what would be the most feasible way to obtain a statistically significant result in a subsequent study?

A) Decrease the mean weight change

B) Increase the sample standard deviation

C) Increase the sample size

D) Decrease the sample size

QUESTION 17 [3 marks]

A study was conducted to understand the effect metoprolol on lowering the heart rate among men and women with atrial fibrillation. A sample of 30 men and 25 women were given the drug and heart rates were measured after 48 hours. The mean heart rate for men was 89 with standard deviation of 10 whereas the mean heart rate was 95 with standard deviation of 12 among women.

Which statistical method you would use to test whether the effect of the drug on heart rate is different for men and women? Explain your choice of test and specify any assumptions that need to be satisfied.

QUESTION 18 [2 marks]

Regardless of your choice of test in Question 17, perform the appropriate parametric test and write conclusion. Make sure you refer to the p-value and confidence interval for the effect in your answer.

QUESTION 19 [3 marks]

‘Standard deviation’ and ‘Standard error’ are two statistical terms that are often confused. Explain in your own words what the difference is between them.

Suppose you are interested in whether participation in extracurricular activity is associated with higher academic achievement. In a sample of 250 students who participated in 2 or more extracurricular activity 147 kids were high achievers (scored 80% or more on the Standardized test) while among 350 students who did not report to participate in any extracurricular activity 168 were high achievers.

Which of the following are the most appropriate null and alternative hypotheses?

A H0: There is an association between participation in extracurricular activities and high scores (80% or more) in standardized testing.

HA: There is no association between participation in extracurricular activities and high scores (80% or more) in standardized testing.

B H0: The proportion of high achievers in the extracurricular group is less than or equal to the proportion of high achieves in the non-extracurricular group.

HA: The proportion of high achievers in the extracurricular group is greater than the proportion of high achieves in the non-extracurricular group.

C H0: The proportion of high achievers in the extracurricular group is equal to the proportion of high achieves in the non-extracurricular group.

HA: The proportion of high achievers in the extracurricular group is not equal to the proportion of high achieves in the non-extracurricular group.

D H0: The proportion of high achievers in the extracurricular group is equal to the proportion of high achieves in the non-extracurricular group.

HA: The proportion of high achievers in the extracurricular group is greater than the proportion of high achieves in the non-extracurricular group.

[2 marks]

QUESTION 8

A parallel-group randomised control trial of a new infertility treatment is being trialled. Women undergoing treatment for infertility were invited to participate and were randomised in a 1:1 ratio to receive either the standard treatment or the intervention (PICSI).

The primary outcome is term live-birth ( = 37 weeks gestational age) within the study follow-up period of 2 years.

The expected term live-birth rate is 24% using the standard treatment. The study aims to detect a 5% increase (from 24% to 29%) in the term live-birth rate in the PICSI treatment group with power 90% and alpha 5%, allowing for a 10% drop-out rate.

Calculate the minimum total recruitment target that will sufficiently power the study.

Note: the numbers below indicate targets that have been rounded up to the nearest 50. Select the best option based on to your Stata/PSPower calculation.

A 1650

B 2750

C 3300

D 3650

QUESTION 9

If the observed difference between groups is larger than expected (i.e. greater than 5%), will the recruitment target still provide the analysis with sufficient power?

QUESTION 10

Burr et al. (1976) tested a new procedure to remove house-dust mites from the bedding of adult asthmatics in attempt to improve subjects' lung function, which was measured by PEFR (peak expiratory flow rate). The trial was a two period cross-over design; the control treatment was dust removal from the living room. The means and standard errors for the continuous variable PEFR in the 32 subjects were:

Treatment group Mean Standard Error

Control 329 litres/min 20.8 litres/min

New procedure 335 litres/min 19.6 litres/min

Differences (Treatment - Control) 6.45 litres/min 5.05 litres/min

The researchers decide to perform a one sample t-test on the differences with a significance level of 5%. Which of the following options is correct?

A The test statistic is 1.3 and the associated p-value is statistically significant.

B The test statistic is 1.3 and the associated p-value is not statistically significant.

C The test statistic is 7.2 and the associated p-value is statistically significant.

D There’s not enough information.

QUESTION 11

A cohort of students of a certain age underwent standardised tests in Maths and English. The top 2.5% of students in each subject were awarded medals.

The scores on the Maths test were normally distributed with mean 55 and standard deviation 10. The scores on the English test were normally distributed with mean 60 and standard deviation 13.

Chloe’s marks were 77 in Maths and 85 in English. Will she receive any medals?

A Chloe will receive a medal for English

B Chloe will receive a medal for Maths

C Chloe will receive a medal for Maths and a medal for English

D Chloe will not receive any medals.

QUESTION 12

The Apgar test is used to evaluate the health of a newborn at 1 minute and 5 minutes after birth. Each of five items is scored between 0 and 2. A total score between 7 and 10 is considered normal, a total score between 4 and 6 indicates the infant requires medical attention, and a total score between 0 and 3 indicates the infant requires immediate resuscitation.

The distribution of Apgar scores of a sample of 100 babies with low birth weight has descriptive summary:

n mean sd min p25 median p75 max

100 6.25 2.43 0 5 7 8 9

Which of the following is NOT true?

A The interquartile range is 3

B The distribution is symmetric

C The range is 9

D There were no infants with a score of 10

QUESTION 13

Brown et. al., Morbidity and mortality in patients randomised to double-blind treatment with a long-acting calcium-channel blocker or diuretic in the INSIGHT study, Lancet 356, 29 July 2000.

Which of the following best describes the type of primary outcome?

A) Continuous

B) Categorical

C) Binary

D) Count

QUESTION 14

A group of 11 patients were recruited for a new weight loss diet regimen. Patients were weighed at baseline before the start of a new diet regimen. At the end of 6 weeks patients were weighed again. The mean and variance of the change in weight after 6 weeks were 0.7 and 1.44. Assume that the change in weight is normally distributed. Researchers are interested in whether there was a significant change in weight from baseline to 6 week followup.

What is the most appropriate hypothesis test for the above scenario?

a) Two sample independent t-test

b) Wilcoxon ranked sum test

c) Chi-squared test

d) One sample t-test

QUESTION 16

If a statistical test fails to show a statistically significant test statistic, what would be the most feasible way to obtain a statistically significant result in a subsequent study?

A) Decrease the mean weight change

B) Increase the sample standard deviation

C) Increase the sample size

D) Decrease the sample size

QUESTION 17 [3 marks]

A study was conducted to understand the effect metoprolol on lowering the heart rate among men and women with atrial fibrillation. A sample of 30 men and 25 women were given the drug and heart rates were measured after 48 hours. The mean heart rate for men was 89 with standard deviation of 10 whereas the mean heart rate was 95 with standard deviation of 12 among women.

Which statistical method you would use to test whether the effect of the drug on heart rate is different for men and women? Explain your choice of test and specify any assumptions that need to be satisfied.

QUESTION 18 [2 marks]

Regardless of your choice of test in Question 17, perform the appropriate parametric test and write conclusion. Make sure you refer to the p-value and confidence interval for the effect in your answer.

QUESTION 19 [3 marks]

‘Standard deviation’ and ‘Standard error’ are two statistical terms that are often confused. Explain in your own words what the difference is between them.

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