#1
What is the mean of the following data set: 2, 4, 6, 8, 10?
6
ExplanationMean is the sum of values divided by the number of values.
#2
What is the median of the following data set: 4, 7, 2, 9, 5?
5
ExplanationMedian is the middle value in a sorted dataset.
#3
What does 'p-value' represent in hypothesis testing?
Probability of rejecting a true null hypothesis
ExplanationP-value is the probability of obtaining results as extreme as observed, assuming the null hypothesis is true.
#4
What is the formula to calculate standard deviation?
√(Σ(x - μ)² / n)
ExplanationStandard deviation measures the amount of variation or dispersion in a set of values.
#5
What does a confidence interval represent in statistics?
The range of values within which the population parameter is likely to fall
ExplanationConfidence interval provides a range of values where we expect the true population parameter to lie with a certain level of confidence.
#6
What is the purpose of a z-test in statistics?
To test the difference between two population means
ExplanationZ-test assesses if the difference between sample and population means is statistically significant.
#7
What is skewness in statistics?
A measure of the degree of symmetry in a distribution
ExplanationSkewness measures the asymmetry of a probability distribution.
#8
In a chi-squared test, if the calculated chi-squared value is greater than the critical chi-squared value, what does it indicate?
Null hypothesis is rejected
ExplanationThe calculated chi-squared value being greater suggests a significant difference, leading to rejecting the null hypothesis.
#9
What is the formula to calculate correlation coefficient (Pearson's r)?
Σ(x - μ)(y - ν) / √(Σ(x - μ)²Σ(y - ν)²)
ExplanationCorrelation coefficient measures the strength and direction of a linear relationship between two variables.
#10
What is the purpose of a one-way ANOVA test?
To compare means of more than two independent groups
ExplanationOne-way ANOVA assesses if there are any statistically significant differences between the means of three or more independent groups.
#11
What is the null hypothesis in a t-test for independent samples?
There is no difference between the means of the two groups
ExplanationNull hypothesis in t-test assumes no significant difference between the means of two independent groups.
#12
What is the purpose of a Mann-Whitney U test?
To compare medians of more than two independent groups
ExplanationMann-Whitney U test assesses if there is a difference between the medians of two independent groups.
#13
What is the F-statistic used for in ANOVA?
To test for differences between group means
ExplanationF-statistic in ANOVA tests if the means of different groups are significantly different.