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Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

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This is a easy difficulty Statistics & Math question, commonly asked during Take-home Project rounds at CVS Health.

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This question is commonly asked for Data Scientist candidates at CVS Health during technical interviews.

Calculate CI and Test Correlation Under Normality

Quick Overview

This question evaluates competency in statistical inference, covering confidence-interval estimation for a normal mean with unknown variance, hypothesis testing for Pearson correlation (including degrees of freedom and p-value interpretation), and calculation of an upper normal quantile, within the domain of Statistics & Math for data scientist roles. It is commonly asked because it probes understanding of sampling distributions, the t-distribution and degrees-of-freedom concepts, correlation significance testing and p-values, and normal quantiles, reflecting a blend of conceptual understanding and practical application of statistical formulas and numeric computation.

Inference on a Mean, Significance of a Correlation, and a Normal Quantile

Assume standard parametric conditions (normality as stated). Show formulas, identify degrees of freedom where relevant, and give clear numeric answers.

(a) 95% CI for a Normal Mean (σ unknown)

You have a simple random sample of size n = 64 from a normal population with unknown variance. The sample mean is x̄ = 102 and the sample standard deviation is s = 16. Compute a 95% confidence interval for the population mean μ. State the exact formula you use and the t critical value's degrees of freedom.

(b) Test Significance of a Correlation

You measure two variables X and Y on n = 100 observations and obtain a sample Pearson correlation r = 0.25. Test H0: ρ = 0 versus H1: ρ ≠ 0 at α = 0.05. Show the test statistic, its degrees of freedom, the two-sided p-value, and your conclusion.

(c) Upper 2.5% Threshold of a Normal Process

A process is normally distributed with mean μ = 50 and standard deviation σ = 5. Find the threshold t such that only the top 2.5% of items exceed t, and interpret this t in context.

Quick Overview

(a) 95% CI for a Normal Mean (σ unknown)

Calculate CI and Test Correlation Under Normality

Quick Overview

Inference on a Mean, Significance of a Correlation, and a Normal Quantile

(a) 95% CI for a Normal Mean (σ unknown)

(b) Test Significance of a Correlation

(c) Upper 2.5% Threshold of a Normal Process

Solution

Comments (0)

Calculate CI and Test Correlation Under Normality

Quick Overview

Inference on a Mean, Significance of a Correlation, and a Normal Quantile

(a) 95% CI for a Normal Mean (σ unknown)

(b) Test Significance of a Correlation

(c) Upper 2.5% Threshold of a Normal Process

Solution

Comments (0)