A psychologist is collecting data on the time it takes to learn a certain task. For 50 randomly selected adult subjects, the sam

Question

1 month ago

7

A psychologist is collecting data on the time it takes to learn a certain task. For 50 randomly selected adult subjects, the sam

ple mean is 16.40 minutes and the sample standard deviation is 4.00 minutes. Construct the 95 percent confidence interval for the mean time required by all adults to learn the task. Assume that X, the time to learn a task, is distributed normally.

Mathematics

1 answer:

zzz [12.3K] · Answer 1 · 2026-04-01T17:22:03+03:00

Response: $(15.263,\ 17.537)$

Step-by-step analysis:

Based on the information provided, we note

Sample size: n= 50

$\overline{x}=16.40$

$s=4.00$

Given that the population standard deviation is not known, a t-test is employed.

Critical value for the 95 percent confidence interval:

$t_{n-1,\alpha/2}=t_{49, 0.025}= 2.009575\approx2.010$

Confidence interval: $\overline{x}\pm t_{n-1, \alpha/2}\dfrac{s}{\sqrt{n}}$

$16.40\pm (2.010)\dfrac{4}{\sqrt{50}}\\\\=16.40\pm1.13702770415\\\\=16.40\pm1.1370\\\\=(16.40-1.1370,\ 16.40+1.1370)\\\\=(15.263,\ 17.537)$

Required 95% confidence interval: $(15.263,\ 17.537)$