Significance Tests for a Proportion

Deciding whether a claim survives the data.

12 problems · about 22 minutes · VAR-6.E, DAT-3.A

NameDate

Figure — use these to answer the problems

Observed against expected under the null. The wider the gap, the harder chance alone is to believe.

Observed62

Expected50

Observed successes62

Expected under the null50

Figure 1

Straightforward practice. Get the method working first.

5 problems

Sample 0.55, p₀ = 0.5, standard error 0.05. What is z?
Answer
2
Which proportion is used to compute the standard error in a test?
- The null value p₀.
- The sample proportion.
p₀ = 0.5, n = 400. Standard error?
Answer
p₀ = 0.5, n = 100. What is np₀?
Answer
Both np₀ and n(1−p₀) must be at least what number?
Answer

The same ideas with more to keep track of.

3 problems

Sample 0.6, p₀ = 0.5, standard error 0.05. What is z?
Answer
p-value 0.016 at alpha 0.05. Reject the null? 1 yes, 0 no.
Answer
Should hypotheses be about the parameter or the statistic? 1 parameter, 2 statistic.
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Put the test procedure in order.
Write 1 to 4 in the boxes to put these in order.
- State hypotheses about the population proportion.
- Check the random, independence and large-sample conditions.
- Compute the test statistic and the p-value.
- Compare to alpha and conclude in context.
p₀ = 0.5, n = 2500. Standard error?
Answer
The Standard Error
p₀ = 0.5 and n = 100. What is the standard error?
Answer
The Statistic
Sample proportion 0.62, p₀ = 0.5, standard error 0.05. What is z?
Answer