The 90% confidence interval for the mean one week amusing time in New York City is 5.22 less than mean less than 5.98 minutes construct a 95% confidence interval based on the same data which interval provides more information

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)) = 2μ = 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.

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

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