Descriptive & Inferential Stats
1
A researcher observes that the mean income in a sample of 500 employees is £45,000 with a standard deviation of £12,000. When calculating a 95% confidence interval for the population mean, which assumption is MOST critical to the validity of this interval, and why?
2
What is the main difference between descriptive and inferential statistics?
3
Which level of measurement has categories with no inherent order?
4
Which chart best displays the distribution of a continuous variable?
5
What is a key feature of probability sampling?
6
Which measure of central tendency is least affected by outliers?
7
What does standard deviation measure?
8
What does a z-score represent?
9
What is a Type I error in hypothesis testing?
10
Which test is typically used for parametric comparisons of means?
11
When is the Chi-Square test appropriate?
12
In a study examining test scores, the distribution is heavily left-skewed with a mean of 78 and median of 82. A researcher must choose between using the mean or median to represent central tendency. Which statement best justifies the choice of median in this context?
13
A quality control manager tests whether a manufacturing process produces items with mean weight of 500g. The null hypothesis is H₀: μ = 500g. After collecting data, the p-value is 0.08. At α = 0.05, the manager fails to reject H₀. Which interpretation correctly reflects the statistical conclusion?
14
A researcher compares three treatment groups using ANOVA and obtains F = 4.2 with p = 0.015. Before concluding which groups differ, what is the most appropriate next step?
Choose one or more answers
15
In a simple linear regression model predicting house prices from square footage, R² = 0.72. Which statement most accurately interprets this coefficient of determination?
16
A sampling distribution of the sample mean is constructed by repeatedly drawing samples of size n = 100 from a population. As the sample size increases to n = 400, how does the standard error of the mean change, and what is the theoretical basis?
17
A dataset contains outliers that inflate the standard deviation to 25. After removing the outliers, the standard deviation becomes 8. Which measure of spread would be LEAST affected by this removal, and why?
18
A researcher conducts a two-sample t-test comparing mean reaction times between two groups. The test assumes equal population variances. If this assumption is violated, which consequence is most likely?
19
In a normal distribution with μ = 100 and σ = 15, approximately what percentage of observations fall between one and two standard deviations above the mean?
20
A researcher uses stratified random sampling to select 600 students from a university with 10,000 students. The university has four faculties with sizes: Science (3,000), Arts (4,000), Engineering (2,000), and Medicine (1,000). How many students should be selected from the Science faculty to maintain proportional representation?
Feedback
Nominal scales categorize without any ranking or order.
Histograms show frequency distribution of a continuous variable.
Probability sampling assigns known selection probabilities to elements.
Median remains stable when extreme values skew the data.
SD quantifies how much values deviate from the mean on average.
Z-score standardizes values relative to the distribution.
Type I is a false positive—detecting an effect when there is none.
t-tests assume normal distribution and equal variances.
Chi-Square assesses if distributions of categorical variables differ.
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