16.07 Confidence intervals
Interactive practice questions
A sample of size $170$170 is taken from the population, and the sample proportion is found to be $0.55$0.55.
| Standard Normal Probability | z-value |
|---|---|
| $0.9$0.9 | $1.282$1.282 |
| $0.925$0.925 | $1.440$1.440 |
| $0.95$0.95 | $1.645$1.645 |
| $0.975$0.975 | $1.960$1.960 |
| $0.99$0.99 | $2.326$2.326 |
| $0.995$0.995 | $2.576$2.576 |
State the $z$z-value that corresponds to a $90%$90% confidence interval.
Use the table of values to calculate the $90%$90% confidence interval for the true proportion.
Express your answer in the form $\left(\editable{},\editable{}\right)$(,), and give your answer to two decimal places.
Which of the following statements about the confidence interval are correct? Select all that apply.
There is a $90%$90% probability that the true proportion lies between $0.49$0.49 and $0.61$0.61.
The probability that the true proportion lies within $\left(0.49,0.61\right)$(0.49,0.61) is $0$0 or $1$1.
We have $90%$90% confidence that the true proportion lies between $0.49$0.49 and $0.61$0.61.
The true proportion lies between $0.49$0.49 and $0.61$0.61.
A sample of size $130$130 is taken from the population, and the sample proportion is found to be $0.69$0.69.
A sample of size $140$140 is taken from the population, and the sample proportion is found to be $0.53$0.53.
A sample of size $180$180 is taken from the population, and the sample proportion is found to be $0.63$0.63.