Q:

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

Accepted Solution

A:
Answer: [tex](15.263,\ 17.537)[/tex]Step-by-step explanation:According to the given information, we have Sample size : n= 50[tex]\overline{x}=16.40[/tex][tex]s=4.00[/tex]Since population standard deviation is unknown, so we use t-test.Critical value for  95 percent confidence interval  :[tex]t_{n-1,\alpha/2}=t_{49, 0.025}= 2.009575\approx2.010[/tex]Confidence interval : [tex]\overline{x}\pm t_{n-1, \alpha/2}\dfrac{s}{\sqrt{n}}[/tex][tex]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)[/tex]Required 95% confidence interval :  [tex](15.263,\ 17.537)[/tex]