Lesson test: Confidence intervals

1.[3p]
What does "95 per cent confidence" describe?

A procedure that captures the true parameter in 95 per cent of repetitions

Correct

The probability that this particular interval contains the parameter

The answer is: A procedure that captures the true parameter in 95 per cent of repetitions

The proportion of the data lying inside the interval

The answer is: A procedure that captures the true parameter in 95 per cent of repetitions

The probability that the estimate equals the parameter

The answer is: A procedure that captures the true parameter in 95 per cent of repetitions

2.[3p]
A sample of 25 has $\overline{x} = 12.4$ and $s = 3.0$ , and $t_{0.975, 24} = 2.064$ . What is the upper end of the 95 per cent interval, to two decimal places?

CorrectNot quite: 13.64

3.[1p]
A 99 per cent confidence interval is wider than a 95 per cent one from the same data.

True

Correct

False

The answer is: True

4.[2p]
What multiplier does a 95 per cent $t$ interval use at 9 degrees of freedom, to three decimal places?

CorrectNot quite: 2.262

5.[2p]
Why does the $t$ distribution have heavier tails than the normal?

The denominator $s$ is itself random, adding variability beyond that of $\overline{X}$

Correct

The population is assumed to be skewed

The answer is: The denominator $s$ is itself random, adding variability beyond that of $\bar{X}$

Small samples have larger population variance

The answer is: The denominator $s$ is itself random, adding variability beyond that of $\bar{X}$

The $t$ distribution has no mean

The answer is: The denominator $s$ is itself random, adding variability beyond that of $\bar{X}$

6.[2p]
A survey of 400 finds 240 in favour. What is the lower end of the Wald interval, to three decimal places?

CorrectNot quite: 0.552

7.[3p]
With 0 successes in 20 trials, the Wald interval is the single point $[0, 0]$ . What is wrong with that?

The estimated standard error is zero, so the procedure claims certainty the data cannot supply

Correct

The sample size is below 30

The answer is: The estimated standard error is zero, so the procedure claims certainty the data cannot supply

The true proportion cannot be zero

The answer is: The estimated standard error is zero, so the procedure claims certainty the data cannot supply

The normal approximation is exact only at $p = 0.5$

The answer is: The estimated standard error is zero, so the procedure claims certainty the data cannot supply

8.[2p]
A trial sees 0 adverse events in 50 patients. What upper rate does the rule of three suggest, as a decimal?

CorrectNot quite: 0.06

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Confidence intervals

1.[3p]
What does "95 per cent confidence" describe?

2.[3p]
A sample of 25 has $\overline{x} = 12.4$ and $s = 3.0$ , and $t_{0.975, 24} = 2.064$ . What is the upper end of the 95 per cent interval, to two decimal places?

3.[1p]
A 99 per cent confidence interval is wider than a 95 per cent one from the same data.

4.[2p]
What multiplier does a 95 per cent $t$ interval use at 9 degrees of freedom, to three decimal places?

5.[2p]
Why does the $t$ distribution have heavier tails than the normal?

6.[2p]
A survey of 400 finds 240 in favour. What is the lower end of the Wald interval, to three decimal places?

7.[3p]
With 0 successes in 20 trials, the Wald interval is the single point $[0, 0]$ . What is wrong with that?

8.[2p]
A trial sees 0 adverse events in 50 patients. What upper rate does the rule of three suggest, as a decimal?

9.[2p]
What sample size gives a margin of 2 percentage points for a proportion near 0.5?

1.[3p] What does "95 per cent confidence" describe?

2.[3p] A sample of 25 has x‾=12.4 and s=3.0, and t0.975,24=2.064. What is the upper end of the 95 per cent interval, to two decimal places?

3.[1p] A 99 per cent confidence interval is wider than a 95 per cent one from the same data.

4.[2p] What multiplier does a 95 per cent t interval use at 9 degrees of freedom, to three decimal places?

5.[2p] Why does the t distribution have heavier tails than the normal?

6.[2p] A survey of 400 finds 240 in favour. What is the lower end of the Wald interval, to three decimal places?

7.[3p] With 0 successes in 20 trials, the Wald interval is the single point [0,0]. What is wrong with that?

8.[2p] A trial sees 0 adverse events in 50 patients. What upper rate does the rule of three suggest, as a decimal?

9.[2p] What sample size gives a margin of 2 percentage points for a proportion near 0.5?

1.[3p]
What does "95 per cent confidence" describe?

2.[3p]
A sample of 25 has $\overline{x} = 12.4$ and $s = 3.0$ , and $t_{0.975, 24} = 2.064$ . What is the upper end of the 95 per cent interval, to two decimal places?

3.[1p]
A 99 per cent confidence interval is wider than a 95 per cent one from the same data.

4.[2p]
What multiplier does a 95 per cent $t$ interval use at 9 degrees of freedom, to three decimal places?

5.[2p]
Why does the $t$ distribution have heavier tails than the normal?

6.[2p]
A survey of 400 finds 240 in favour. What is the lower end of the Wald interval, to three decimal places?

7.[3p]
With 0 successes in 20 trials, the Wald interval is the single point $[0, 0]$ . What is wrong with that?

8.[2p]
A trial sees 0 adverse events in 50 patients. What upper rate does the rule of three suggest, as a decimal?

9.[2p]
What sample size gives a margin of 2 percentage points for a proportion near 0.5?