Ask Question
16 June, 12:29

The 90% confidence interval for the mean one-way commuting time in New York City is

5.22 < μ < 5.98 minutes. Construct a 95% interval based on the same data. Which interval provides more information.

+4
Answers (1)
  1. 16 June, 14:45
    0
    The 90% confidence interval is given by mean - 1.645 (s. d. / sqrt (n)) < μ < mean + 1.645 (s. d. / sqrt (n))

    mean - 1.645 (s. d. / sqrt (n)) + mean + 1.645 (s. d. / sqrt (n)) = 2 μ = 5.22 + 5.98 = 11.2

    μ = 11.2 / 2 = 5.6

    Thus, mean - 1.645 (s. d. / sqrt (n)) = 5.6 - 1.645 (s. d. / sqrt (n)) = 5.22

    5.6 - 5.22 = 1.645 (s. d. / sqrt (n)) = 0.38

    s. d. / sqrt (n) = 0.38 / 1.645 = 0.231

    The 95% confidence interval is given by mean - 1.96 (s. d. / sqrt (n)) < μ < mean + 1.96 (s. d. / sqrt (n)) = 5.6 - 1.96 (0.231) < μ < 5.6 + 1.96 (0.231) = 5.6 - 0.4528 < μ < 5.6 + 0.4528 = 5.15 < μ < 6.05

    The 95% confidence interval provides more information because it has a larger interval.
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “The 90% confidence interval for the mean one-way commuting time in New York City is 5.22 < μ < 5.98 minutes. Construct a 95% interval based ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers