All Free Statistics MCQs with Answers

• A. stating H1
• B. stating Ho
• C. L of significance
• D. Test statistics

Explanation: Hypothesis testing begins by formulating the null hypothesis and the alternative hypothesis; among the choices, stating H₀ is the first step. Significance level and test statistic are selected or calculated afterward.

• A. Q Qo
• B. Q ≠ Qo
• C. None of these

Explanation: When the null hypothesis specifies equality, H₀: Q = Q₀, the general two-sided alternative is H₁: Q ≠ Q₀. A one-sided alternative would require the question to state a direction such as greater than or less than.

• A. Q ≤ Qo
• B. Q ≥ Qo
• C. Q = Qo
• D. Q ≠ Qo

Explanation: The null hypothesis contains the equality component, either explicitly or as part of an inequality such as Q ≤ Q₀ or Q ≥ Q₀. A strict inequality Q ≠ Q₀ is therefore used as an alternative hypothesis.

• A. Rejected when it is true
• B. Rejected when it is false
• C. Accepted when it is true
• D. Accepted when it is false

Explanation: A Type II error occurs when a false null hypothesis is not rejected, often loosely described as accepting H₀ when it is false. Rejecting a true null hypothesis is instead a Type I error.

• A. Composite hypothesis
• B. Alternative hypothesis
• C. Null hypothesis
• D. Simple hypothesis

Explanation: The null hypothesis is the specific claim tested against sample evidence, usually representing no effect or no difference. The alternative hypothesis states the competing claim and is supported only when the null is rejected.

• A. r + c
• B. rc
• C. ι r - c ι
• D. (r -1) (c -1)

Explanation: For an r × c contingency table, the degrees of freedom are obtained by multiplying the numbers of independent row and column categories: (r−1)(c−1).

• A. Simple average of relatives
• B. Average of weights
• C. Weighted average of relatives
• D. All of above

Explanation: The household budget method calculates CPI as a weighted average of price relatives, with household expenditure shares serving as weights. A simple average of relatives gives equal importance to all items and is therefore a different method.

• A. Household price index
• B. Retail price index
• C. Both a and b
• D. None of these

Explanation: CPI is commonly called the retail price index because it measures changes in prices paid by consumers, and it may also be described as a household price index. Terminology varies by country, but both listed descriptions are used in this context.

• A. Quantity index number
• B. Price index number
• C. Value index number
• D. None of these

Explanation: Price index numbers are most widely used because they measure changes in the general price level and inflation. Quantity and value indices are useful, but they are less commonly used for this broad purpose.

• A. Place
• B. Yearly
• C. Time
• D. None

Explanation: A time series arranges observations in chronological order, such as daily, monthly, or yearly values. Yearly data are only one possible form of a time series, so time is the broader answer.