An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an estimate at the 98% level of confidence. For a sample of 4386 third graders, the mean words per minute read was 28.1. Assume a population standard deviation of 5.7. Construct the confidence interval for the mean number of words a third grader can read per minute. Round your answers to one decimal place.

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AlonsoDehner AlonsoDehner · Answer 1 · 2020-02-01T10:20:32+01:00

Answer:

confidence interval = (27.9, 28.3)

Step-by-step explanation:

Here we are given the population std deviation value as 5.7. So we can use Z critical value for finding out confidence interval.

Sample size n = 4386

Std error of sample mean = [tex]\frac{5.7}{\sqrt{4386} } \\=0.0861[/tex]

Sample mean = 28.1

Z critical value two tailed for 98% = 2.326

margin of error = ±2.326*0.0861 =0.2003

confidence interval lower bound

=[tex]28.1-0.2003=27.8997[/tex]

Upper bound

= [tex]28.1+0.2003\\=28.3003[/tex]

After rounding off we get

confidence interval = (27.9, 28.3)