stats ch 9 sec 2
Determine whether the following statement is true or false. To construct a confidence interval about the mean, the population from which the sample is drawn must be approximately normal.
false
To select the correct Student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?
n-1
Determine the t-value in each of the cases. -Find the t-value such that the area in the right tail is 0.01 with 21 degrees of freedom. -Find the t-value such that the area in the right tail is 0.05 with 12 degrees of freedom. -Find the t-value such that the area left of the t-value is 0.025 with 21 degrees of freedom. [Hint: Use symmetry.] -Find the critical t-value that corresponds to 96% confidence. Assume 27 degrees of freedom.
- 2.518 - 1.782 - -2.080 - 2.158
What is the area under the graph of every Student's t-distribution?
1
A trade magazine routinely checks the drive-through service times of fast-food restaurants. An 80% confidence interval that results from examining 561 customers in one fast-food chain's drive-through has a lower bound of 164.7 seconds and an upper bound of 168.1 seconds. What does this mean?
One can be 80% confident that the mean drive-through service time of this fast-food chain is between 164.7 seconds and 168.1 seconds.
Which of the following is not a characteristic of Students' t-distribution?
The t-distribution has a mean of 1.
Explain why the t-distribution has less spread as the number of degrees of freedom increases.
The t-distribution has less spread as the degrees of freedom increase because, as n increases, s becomes closer to σ by the law of large numbers.
Which of the following would be a correct interpretation of a 99% confidence interval such as 4.1<μ<5.6?
We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of μ.
Which of the following is NOT an equivalent expression for the confidence interval given by 161.7<μ<189.5?
161.7±27.8
Determine the critical value tα/2 that corresponds to a 95% confidence level with 12 degrees of freedom. Round to the nearest thousandth.
2.179
The margin of error of a confidence interval for μ depends on three factors. What are they?
Standard deviation of the population Level of confidence Sample size
Determine the point estimate of the population mean and margin of error for the confidence interval. Lower bound is 21, upper bound is 25.
The point estimate of the population mean is 23 The margin of error for the confidence interval is 22.
A poll was conducted that asked 1017 people how many books they had read in the past year. Results indicated that x=10.6 books and s=16.6 books. Construct a 99% confidence interval for the mean number of books people read.
(9.26,11.94)
