A researcher increases the sample size of a survey from 100 to 400 while the standard deviation stays the same. What happens to the standard error of the mean?

It falls to half its previous value

A trial in 4,000 hypertensive adults finds that a new counselling package lowers systolic pressure by 1 mm Hg more than usual care (p < 0.001). The best interpretation is that the result is:

Statistically significant but of little clinical importance

Clinically important because the p value is very small

Not significant because the difference is only 1 mm Hg

Invalid because samples above 1,000 cannot be tested

The power of a statistical test is the probability of:

Detecting a true difference when it exists

Accepting the null hypothesis when it is true

Rejecting the null hypothesis when it is true

Biostatistics and data analysis

30 M.Sc Nursing Entrance (AIIMS, LBS, PGIMER, JIPMER) practice questions on Biostatistics and data analysis, part of Nursing Research and Statistics. The first 25 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

Question 1 · Medium
A researcher increases the sample size of a survey from 100 to 400 while the standard deviation stays the same. What happens to the standard error of the mean?
1. AIt falls to half its previous value
2. BIt does not change
3. CIt is reduced to one quarter
4. DIt is doubled
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Answer: A · It falls to half its previous value
The standard error of the mean equals SD divided by the square root of n. Raising n fourfold raises the square root of n twofold, so the standard error falls to half. The confidence interval narrows by the same factor. Precision therefore improves with the square root of the sample size, not in direct proportion.
- B: The standard error depends on n, unlike the standard deviation of the data.
- C: A quarter would follow only if SE fell in direct proportion to n, ignoring the square root.
- D: A larger sample makes the estimate more precise, so the standard error cannot rise.
Question 2 · Hard
Pain is scored 0-10 in patients from three wards (n = 12, 15 and 10). The scores are clearly skewed, and a normality test is significant in two of the wards. Which test should compare the wards?
1. AKruskal-Wallis H test
2. BFriedman test
3. COne-way ANOVA
4. DMann-Whitney U test
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Answer: A · Kruskal-Wallis H test
There are three independent groups, and the ordinal, non-normal scores in small samples violate the assumptions of ANOVA. The Kruskal-Wallis test ranks all observations together and compares the mean ranks of the groups. It is the non-parametric counterpart of one-way ANOVA. A significant result is followed by pairwise rank tests with a corrected alpha.
- B: Friedman is for three or more related (repeated) measurements on the same subjects.
- C: ANOVA assumes approximately normal data, which these small skewed samples do not meet.
- D: Mann-Whitney compares only two independent groups at a time.
Question 3 · Medium
A trial in 4,000 hypertensive adults finds that a new counselling package lowers systolic pressure by 1 mm Hg more than usual care (p < 0.001). The best interpretation is that the result is:
1. AClinically important because the p value is very small
2. BNot significant because the difference is only 1 mm Hg
3. CInvalid because samples above 1,000 cannot be tested
4. DStatistically significant but of little clinical importance
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Answer: D · Statistically significant but of little clinical importance
With very large samples even trivial differences reach statistical significance. The p value shows that the difference is unlikely to be chance, not that it matters to patients. A 1 mm Hg fall in systolic pressure is too small to change care for an individual. Clinical significance is judged from the effect size and its confidence interval.
- A: A small p value reflects the sample size and certainty, not the size or importance of the effect.
- B: Statistical significance is set by the p value, which here is below 0.001.
- C: Large samples are an advantage for precision, not a reason to reject a test.
Question 4 · Easy
The power of a statistical test is the probability of:
1. ADetecting a true difference when it exists
2. BObtaining a p value below 0.01
3. CAccepting the null hypothesis when it is true
4. DRejecting the null hypothesis when it is true
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Answer: A · Detecting a true difference when it exists
Power equals 1 minus beta, where beta is the probability of a Type II error (missing a real effect). Most nursing studies aim for a power of at least 0.80. Power rises with a larger sample, a larger effect size and a higher alpha. A power analysis is therefore done before data collection to fix the sample size.
- B: A p value below a cut-off is a result of one study, not the property of the test.
- C: Correctly retaining a true null hypothesis has probability 1 minus alpha, not power.
- D: Rejecting a true null hypothesis is a Type I error, whose probability is alpha.
Question 5 · Hard
A survey of 100 adults attending a rural PHC finds a mean systolic blood pressure of 140 mm Hg with a standard deviation of 20 mm Hg. What is the 95% confidence interval for the population mean?
1. A138.0 to 142.0 mm Hg
2. B136.1 to 143.9 mm Hg
3. C100.8 to 179.2 mm Hg
4. D134.8 to 145.2 mm Hg
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Answer: B · 136.1 to 143.9 mm Hg
The standard error is SD divided by the square root of n: 20 / 10 = 2 mm Hg. The 95% interval is the mean plus or minus 1.96 x SE: 140 plus or minus 3.92, giving 136.1 to 143.9 mm Hg. Using the SD instead of the SE gives the range expected for individual readings, not the mean. Using 2.58 gives the wider 99% interval.
- A: Adding and subtracting one SE gives only about a 68% interval.
- C: Using 1.96 x SD (39.2) describes individual values, not the precision of the mean.
- D: Using 2.58 x SE (5.16) gives the 99% interval, not the 95% interval.
Question 6 · Easy
Which correlation coefficient is appropriate when both variables are measured on an ordinal scale?
1. ASpearman's rank correlation
2. BPhi coefficient
3. CPearson's product-moment correlation
4. DPoint-biserial correlation
Answer and explanation in LearnFree account
Question 7 · Easy
Which measure of central tendency changes the most when one extremely high value is added to a small data set?
1. AMean
2. BMidpoint of the middle two values
3. CMode
4. DMedian
Answer and explanation in LearnFree account
Question 8 · Hard
In a large population, fasting blood glucose is normally distributed with a mean of 90 mg/dL and a standard deviation of 8 mg/dL. Approximately what percentage of adults will have a value above 106 mg/dL?
1. AAbout 16%
2. BAbout 0.5%
3. CAbout 2.5%
4. DAbout 5%
Answer and explanation in LearnFree account
Question 9 · Medium
In a pilot study of 24 patients, a 2 x 2 table of catheter type against urinary infection has two cells with expected frequencies below 5. Which test should replace the chi-square test?
1. APearson's correlation
2. BFisher's exact probability test
3. CIndependent-samples t test
4. DMcNemar test
Answer and explanation in LearnFree account
Question 10 · Medium
A trial of a breathing exercise reports a lower mean anxiety score in the intervention group, with p = 0.02. What does this p value mean?
1. AIf there were truly no difference, a result this large would occur about 2% of the time
2. BThere is a 2% probability that the null hypothesis is true
3. CThere is a 98% probability that the breathing exercise is effective
4. DOnly 2% of patients in the intervention group failed to improve
Answer and explanation in LearnFree account
Question 11 · Medium
A one-way ANOVA comparing mean pain scores under four analgesic regimens gives a significant F ratio (p = 0.01). The next step to find which regimens differ is to:
1. AApply a chi-square test to the four means
2. BApply a post hoc test such as Tukey's
3. CReport that all four regimens differ from one another
4. DRepeat the ANOVA with a larger sample
Answer and explanation in LearnFree account
Question 12 · Easy
In a perfectly symmetrical normal distribution, the mean, median and mode are:
1. AIn the order mode > median > mean
2. BIn the order mean > median > mode
3. CEqual to one another
4. DSeparated by one standard deviation each
Answer and explanation in LearnFree account
Question 13 · Medium
A nurse researcher planning a trial wants to reduce the required sample size, with everything else unchanged. Which change achieves this?
1. ALowering alpha from 0.05 to 0.01
2. BRaising the desired power from 80% to 90%
3. CChoosing a more variable outcome measure
4. DExpecting a larger effect size
Answer and explanation in LearnFree account
Question 14 · Hard
In a study of 200 post-operative wounds, 80 patients received a silver dressing and 120 a plain dressing; 50 wounds became infected in all. Under the null hypothesis of no association, what is the expected number of infected wounds in the silver-dressing group?
1. A40
2. B30
3. C25
4. D20
Answer and explanation in LearnFree account
Question 15 · Hard
Instead of ANOVA, a student compares three teaching methods using three separate t tests, each at alpha = 0.05. Assuming the tests are independent, what is the probability of at least one false-positive result?
1. AAbout 0.01%
2. BExactly 5%
3. CAbout 14%
4. DAbout 86%
Answer and explanation in LearnFree account
Question 16 · Easy
What are the mean and standard deviation of the standard normal (z) distribution?
1. AMean 1, standard deviation 0
2. BMean 50, standard deviation 10
3. CMean 0, standard deviation 0.5
4. DMean 0, standard deviation 1
Answer and explanation in LearnFree account
Question 17 · Medium
When a 99% confidence interval for a population mean is built from a large sample, the standard error is multiplied by approximately:
1. A1.96
2. B3.29
3. C2.58
4. D1.64
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Question 18 · Hard
A community health nurse plans a survey to estimate the prevalence of anaemia among adolescent girls in a block. Earlier surveys suggest a prevalence of 20%, and she wants an absolute precision of 4 percentage points. Using n = 4pq / d squared, what sample size is needed?
1. A1,600
2. B10,000
3. C400
4. D100
Answer and explanation in LearnFree account
Question 19 · Hard
On a knowledge test, 20 staff nurses of ward A have a mean score of 30 and 30 staff nurses of ward B have a mean score of 40. What is the combined mean score of all 50 nurses?
1. A36
2. B35
3. C38
4. D34
Answer and explanation in LearnFree account
Question 20 · Easy
Which test is the non-parametric alternative to the independent-samples t test?
1. AKruskal-Wallis test
2. BMann-Whitney U test
3. CMcNemar test
4. DWilcoxon signed-rank test
Answer and explanation in LearnFree account
Question 21 · Hard
A researcher cross-tabulates three hospital wards against four categories of patient satisfaction (very satisfied, satisfied, dissatisfied, very dissatisfied) and applies the chi-square test. How many degrees of freedom does the test have?
1. A11
2. B6
3. C12
4. D5
Answer and explanation in LearnFree account
Question 22 · Easy
Which portion of the observations is contained within the interquartile range?
1. AThe middle 68%
2. BThe middle 50% of values
3. CThe lowest 25%
4. DThe middle 95%
Answer and explanation in LearnFree account
Question 23 · Medium
A study of a new oral care protocol reports a mean reduction in plaque score of 3.2 points compared with routine care, 95% CI -1.5 to 7.9. At the 0.05 level, this result is:
1. AStatistically significant, because most of the interval is above zero
2. BStatistically significant, because the mean difference is positive
3. CNot statistically significant, because the interval includes zero
4. DNot interpretable without the standard deviation of each group
Answer and explanation in LearnFree account
Question 24 · Hard
In 60 bedridden patients, the presence or absence of a pressure injury is recorded before and after a two-week repositioning programme, giving a 2 x 2 table of the same patients. Which test is appropriate?
1. AMcNemar test
2. BFisher's exact test
3. CPaired t test
4. DChi-square test of independence
Answer and explanation in LearnFree account
Question 25 · Easy
The standard deviation of a set of observations is:
1. AThe square root of the variance
2. BThe square of the variance
3. CThe variance divided by the mean
4. DThe mean of the absolute deviations
Answer and explanation in LearnFree account

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Biostatistics and data analysis

A researcher increases the sample size of a survey from 100 to 400 while the standard deviation stays the same. What happens to the standard error of the mean?

Pain is scored 0-10 in patients from three wards (n = 12, 15 and 10). The scores are clearly skewed, and a normality test is significant in two of the wards. Which test should compare the wards?

A trial in 4,000 hypertensive adults finds that a new counselling package lowers systolic pressure by 1 mm Hg more than usual care (p < 0.001). The best interpretation is that the result is:

The power of a statistical test is the probability of:

A survey of 100 adults attending a rural PHC finds a mean systolic blood pressure of 140 mm Hg with a standard deviation of 20 mm Hg. What is the 95% confidence interval for the population mean?

Which correlation coefficient is appropriate when both variables are measured on an ordinal scale?

Which measure of central tendency changes the most when one extremely high value is added to a small data set?

In a large population, fasting blood glucose is normally distributed with a mean of 90 mg/dL and a standard deviation of 8 mg/dL. Approximately what percentage of adults will have a value above 106 mg/dL?

In a pilot study of 24 patients, a 2 x 2 table of catheter type against urinary infection has two cells with expected frequencies below 5. Which test should replace the chi-square test?

A trial of a breathing exercise reports a lower mean anxiety score in the intervention group, with p = 0.02. What does this p value mean?

A one-way ANOVA comparing mean pain scores under four analgesic regimens gives a significant F ratio (p = 0.01). The next step to find which regimens differ is to:

In a perfectly symmetrical normal distribution, the mean, median and mode are:

A nurse researcher planning a trial wants to reduce the required sample size, with everything else unchanged. Which change achieves this?

In a study of 200 post-operative wounds, 80 patients received a silver dressing and 120 a plain dressing; 50 wounds became infected in all. Under the null hypothesis of no association, what is the expected number of infected wounds in the silver-dressing group?

Instead of ANOVA, a student compares three teaching methods using three separate t tests, each at alpha = 0.05. Assuming the tests are independent, what is the probability of at least one false-positive result?

What are the mean and standard deviation of the standard normal (z) distribution?

When a 99% confidence interval for a population mean is built from a large sample, the standard error is multiplied by approximately:

A community health nurse plans a survey to estimate the prevalence of anaemia among adolescent girls in a block. Earlier surveys suggest a prevalence of 20%, and she wants an absolute precision of 4 percentage points. Using n = 4pq / d squared, what sample size is needed?

On a knowledge test, 20 staff nurses of ward A have a mean score of 30 and 30 staff nurses of ward B have a mean score of 40. What is the combined mean score of all 50 nurses?

Which test is the non-parametric alternative to the independent-samples t test?

A researcher cross-tabulates three hospital wards against four categories of patient satisfaction (very satisfied, satisfied, dissatisfied, very dissatisfied) and applies the chi-square test. How many degrees of freedom does the test have?

Which portion of the observations is contained within the interquartile range?

A study of a new oral care protocol reports a mean reduction in plaque score of 3.2 points compared with routine care, 95% CI -1.5 to 7.9. At the 0.05 level, this result is:

In 60 bedridden patients, the presence or absence of a pressure injury is recorded before and after a two-week repositioning programme, giving a 2 x 2 table of the same patients. Which test is appropriate?

The standard deviation of a set of observations is: