Scientific Officer-Statistics -Practice-1

Practice questions

1. A population has a mean of 50 and a standard deviation of 10. If an observation is 70, what is its standard score (z-score)?
   • 1
   • 2
   • 3
   • 4
2. A random variable follows a binomial distribution with n = 5 and probability of success p = 0.4. What is the probability of exactly two successes?
   • 0.2304
   • 0.3456
   • 0.4000
   • 0.5000
3. In a normal distribution, approximately what percentage of observations lies within one standard deviation of the mean?
   • 50%
   • 68%
   • 95%
   • 99.7%
4. A researcher selects every tenth household after randomly selecting the first household from the first ten. Which sampling method is being used?
   • Stratified random sampling
   • Cluster sampling
   • Systematic sampling
   • Purposive sampling
5. A population is divided into urban and rural groups, and random samples are selected separately from each group. This is:
   • Simple random sampling
   • Stratified random sampling
   • Systematic sampling
   • Convenience sampling
6. What happens to the standard error of the sample mean when the sample size increases, assuming the population standard deviation remains constant?
   • It increases
   • It decreases
   • It remains unchanged
   • It becomes equal to the population mean
7. A 95% confidence interval for a population mean is calculated as (42, 48). Which interpretation is statistically appropriate?
   • There is a 95% probability that the fixed population mean changes between 42 and 48
   • The method used would capture the true population mean in approximately 95% of repeated samples
   • Exactly 95% of all population observations lie between 42 and 48
   • The sample mean must be exactly 45 in every repeated sample
8. In hypothesis testing, a Type I error occurs when a researcher:
   • Fails to reject a false null hypothesis
   • Rejects a true null hypothesis
   • Accepts every alternative hypothesis
   • Uses an unnecessarily large sample
9. A statistical test produces a p-value of 0.03. At a significance level of 0.05, what is the appropriate decision?
   • Reject the null hypothesis
   • Accept the null hypothesis as certainly true
   • Increase the significance level to 0.10
   • Conclude that the alternative hypothesis has a 97% probability of being true
10. Which statistical test is generally used to compare the means of two independent groups when population variances are unknown?
    • Independent-samples t-test
    • Paired-samples t-test
    • Chi-square goodness-of-fit test
    • One-sample proportion test
11. Which test is appropriate for examining whether two categorical variables are associated in a contingency table?
    • Pearson chi-square test of independence
    • One-sample t-test
    • Pearson correlation test for continuous variables
    • Paired-samples t-test
12. In simple linear regression, the coefficient of determination (R²) measures:
    • The proportion of variation in the response variable explained by the fitted regression model
    • The average difference between two sample means
    • The probability that the regression coefficient is zero
    • The number of independent variables in the model
13. If the Pearson correlation coefficient between two variables is −0.90, what does this indicate?
    • A strong positive linear relationship
    • A weak negative linear relationship
    • A strong negative linear relationship
    • No linear relationship
14. In a one-way analysis of variance (ANOVA), the null hypothesis states that:
    • All population group means are equal
    • All population variances are necessarily zero
    • Every sample observation is identical
    • At least one population mean must be greater than all others
15. Which probability distribution is commonly used to model the number of events occurring in a fixed interval when events occur independently at a constant average rate?
    • Normal distribution
    • Poisson distribution
    • Uniform distribution
    • Student's t-distribution
16. In a simple random sample of size 100, the sample mean is 40 and the population standard deviation is known to be 10. What is the standard error of the sample mean?
    • 0.5
    • 1
    • 5
    • 10
17. Which condition is essential for using the paired-samples t-test?
    • The two sets of observations must come from unrelated groups
    • Each observation in one condition must be meaningfully paired with an observation in the other condition
    • Both samples must contain exactly the same numerical values
    • The dependent variable must be categorical
18. In experimental design, randomization primarily helps to:
    • Eliminate all measurement errors
    • Reduce systematic bias in assigning treatments to experimental units
    • Guarantee that every treatment produces identical results
    • Remove the need for replication
19. Bayes' theorem is used to calculate:
    • A conditional probability using prior probability and observed evidence
    • The arithmetic mean of a frequency distribution
    • The standard deviation of a normal distribution
    • The rank of a regression matrix
20. A dataset has the values 2, 4, 6, 8 and 10. What is its population variance?
    • 4
    • 6
    • 8
    • 10