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MMLU-Pro / 7884 / 9.6-111. Let X and Y have a bivariate normal distribution with correlation…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

9.6-111. Let XX and YY have a bivariate normal distribution with correlation coefficient ρ\rho. To test H0:ρ=0H_0: \rho=0 against H1:ρ≠0H_1: \rho \neq 0, a random sample of nn pairs of observations is selected. Suppose that the sample correlation coefficient is r=0.68r=0.68. Using a significance level of α=0.05\alpha=0.05, find the smallest value of the sample size nn so that H0H_0 is rejected.
Plain-text mathematical notation (without MathML)
9.6-111. Let X and Y have a bivariate normal distribution with correlation coefficient ρ. To test H₀:ρ=0 against H₁:ρ≠0, a random sample of n pairs of observations is selected. Suppose that the sample correlation coefficient is r=0.68. Using a significance level of α=0.05, find the smallest value of the sample size n so that H₀ is rejected.
Original LaTeX notation
9.6-111. Let $X$ and $Y$ have a bivariate normal distribution with correlation coefficient $\rho$. To test $H_0: \rho=0$ against $H_1: \rho \neq 0$, a random sample of $n$ pairs of observations is selected. Suppose that the sample correlation coefficient is $r=0.68$. Using a significance level of $\alpha=0.05$, find the smallest value of the sample size $n$ so that $H_0$ is rejected.

category

math

options

  1. $9$
  2. $7$
  3. $10$
  4. $11$
  5. $13$
  6. $20$
  7. $5$
  8. $8$
  9. $12$
  10. $15$

src

scibench-stat

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Source and history

upstream_id / Original problem ID
7884
task_id
53100718-6bca-57a3-adb4-2852f59b40da
task_key
default--test--7884
task_revision_id
1
config / split
default / test

Official source

initial import