Question

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

Answer 1

The 95% confidence interval based on the same data is 5.15 < μ < 6.05

Because it has a longer interval, the 95 percent confidence interval offers more details.

What is a confidence interval?

The likelihood that a parameter will fall between two values near the mean is shown by a confidence interval.

Confidence intervals quantify how certain or uncertain a sampling technique is.

Confidence intervals are used by statisticians to gauge the degree of uncertainty in a sample variable.

The 90% confidence interval is given by:

Mean - 1.645(S.D./$\sqrt{n}$) < μ < Mean + 1.645(S.D./$\sqrt{n}$)

2μ = 5.22 + 5.98 = 11.2

μ = 11.2 / 2 = 5.6

Thus,

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.

Learn more about confidence intervals here:

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