A university is trying to accommodate its commuter students in its course scheduling. In a survey, the school asked a sample of 75 randomly chosen students how long their daily commute is, in minutes. The data showed a 90% confidence interval of for the mean commute time for students at the university. Is the following conclusion valid? If 100 more surveys are conducted (each using a sample with members chosen randomly and independently), it is expected that exactly 100 of them will each produce a 90% confidence interval that contains its sample mean. Choices: (A)yes (B)no

Definition of 90% Confidence Interval: A 90% confidence interval means that we expect 90% of the confidence intervals from repeated samples to contain the true population mean, not necessarily the sample mean.Expectation from Additional Surveys: If 100 more surveys are conducted, we expect around 90 of them (90%) to contain the true population mean within their confidence intervals, not all 100.Misunderstanding of Confidence Interval: The conclusion that exactly 100 out of 100 surveys will contain their sample mean within the 90% confidence interval is incorrect because it misunderstands the meaning of a confidence interval.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A university is trying to accommodate its commuter students in its course scheduling. In a survey, the school asked a sample of $75$ randomly chosen students how long their daily commute is, in minutes. The data showed a $90\%$ confidence interval of for the mean commute time for students at the university. $\newline$ Is the following conclusion valid? $\newline$ If $100$ more surveys are conducted (each using a sample with members chosen randomly and independently), it is expected that exactly $100$ of them will each produce a $90\%$ confidence interval that contains its sample mean. $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no $\newline$

View step-by-step help

Home

Math Problems

Algebra 2

Interpret confidence intervals for population means

Full solution

Q. A university is trying to accommodate its commuter students in its course scheduling. In a survey, the school asked a sample of

75

randomly chosen students how long their daily commute is, in minutes. The data showed a

90\%

confidence interval of for the mean commute time for students at the university.

\newline

Is the following conclusion valid?

\newline

100

more surveys are conducted (each using a sample with members chosen randomly and independently), it is expected that exactly

100

of them will each produce a

90\%

confidence interval that contains its sample mean.

\newline

Choices:

\newline

(A)yes

\newline

(B)no

\newline

Definition of $90\%$ Confidence Interval: A $90\%$ confidence interval means that we expect $90\%$ of the confidence intervals from repeated samples to contain the true population mean, not necessarily the sample mean.
Expectation from Additional Surveys: If $100$ more surveys are conducted, we expect around $90$ of them ( $90\%$ ) to contain the true population mean within their confidence intervals, not all $100$ .
Misunderstanding of Confidence Interval: The conclusion that exactly $100$ out of $100$ surveys will contain their sample mean within the $90\%$ confidence interval is incorrect because it misunderstands the meaning of a confidence interval.