IB Mathematics Applications & Interpretation Question Type 1: Assessing the Quality of Questioning Exercises

Determine the minimum sample size required for a 95% confidence interval for a proportion with a margin of error of $\pm 3\%$, assuming $p=0.5$.

Identify the bias in the question "Isn’t school bad?" and rewrite it as a neutral survey question.

Calculate the 95% margin of error for estimating a proportion from a simple random sample of size $n=400$, assuming $p=0.5$.

Identify the sampling method and explain one potential bias in the following procedure:

“Survey every 10th name in the phone directory to gauge customer satisfaction.”

A survey of $1000$ people yields $600$ respondents, $60\%$ of whom support measure X. Assuming nonrespondents differ by $\pm 10\%$ in support, find the possible range for the true support in the population.

A student is designing a questionnaire to investigate spending habits. They draft the following question:

"In your opinion, how significant do you find the majority of the overall economic factors affecting your monthly expenditures?"

(a) Identify two issues with the wording of this question. [2]

(b) Suggest a revised version of the question that improves clarity and includes a suitable response scale. [1]

If a survey historically has a $25\%$ response rate and you need at least $400$ completed surveys, how many people should you contact?

A researcher is designing a survey to investigate student study habits. They initially propose the following question:

"How much do you study?"

(a) Classify this question by type.

(b) Explain one disadvantage of using this question type for a large-scale survey.

(c) Rewrite the question as a structured question using an exhaustive ordinal scale for the number of hours studied per week.

A Likert scale provides options: Strongly agree, Agree, and Neutral. Identify the issue and propose a balanced five-point scale.

In a weighted survey, three age groups have sample sizes, weights, and mean responses as follows:

• Group A: $n_A=100,w_A=1.5,{\bar{x}}_A=4.2$
• Group B: $n_B=150,w_B=1.0,{\bar{x}}_B=3.8$
• Group C: $n_C=50,w_C=2.0,{\bar{x}}_C=4.5$

Compute the overall weighted mean.

Explain why the question “Do you like mathematics and science?” is flawed and rewrite it to avoid double-barreling. [3 marks]

Examine the following answer choices for "How often do you exercise?": A. Daily B. Often C. Sometimes D. Rarely

Identify the issue with these categories and propose corrected, mutually exclusive frequency ranges.