Answer to Question #120258 in Statistics and Probability for Joseph Se

Question

Inferential.

A company offering online speed reading courses claims that students who take their courses show a 5 times (500%) increase in the number of words they can read in a minute without losing comprehension. A random sample of 100 students yielded an average increase of 415% with a standard deviation of 220%.

Calculate a 95% confidence interval for the average increase in number of words students can read in a minute without losing comprehension. Choose the closest answer.

A. (371.88, 458.12)
B.(378.7, 451.3)
C.(411.37, 418.63)
D.(412.09, 417.91)

Answer 1

The critical value for $\alpha=0.05$ is $z_c=z_{1-\alpha/2}=1.96$.

The corresponding confidence interval is computed as shown below:

$$CI=(\bar{X}-z_c\times{\sigma\over \sqrt{n}},\bar{X}+z_c\times{\sigma\over \sqrt{n}})=$$

$$=(415-1.96\times{220\over \sqrt{100}}, 415+1.96\times{220\over \sqrt{100}})=$$

$$=(371.88, 458.12)$$

A. (371.88, 458.12)