Voters in two towns were polled about what party they would support in the upcoming election.  In town A, 120 of the 200 people polled indicated that they were likely to vote for Labor. In town B, 60 of the 150 people polled indicated Labor.

The standard error in the difference (A-B) between the proportions was calculated to be 0.053.

Are the towns different? What is the 99% confidence interval for the difference between the proportions the populations of these 2 towns (A-B) in their voting intentions?

A simple random sample of 500 adults were surveyed to find whether they favoured the sale of Telstra. 332 replied "no". The standard error, correct to three decimal places, of the sample proportion of adults who would reply "no" is

Let p be the proportion of adults who have shares in Telstra. A researcher wishes to test the hypothesis that 60% of adults have shares in Telstra against the alternative that a different percentage of adults have shares in Telstra.

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion.

Construct a 95% confidence interval for the percentage of all adults who have high blood pressure.

In testing the hypothesis that 70% of voters are in favour of tax cuts against the alternative that more than 70% of voters are in favour of tax cuts, researchers found that 310 out of 407 people surveyed were in favour of tax cuts.

A one-proportion z-test is to be carried out. Determine the z-statistic for the test, correct to two decimal places.

A 95% confidence interval for the proportion p of voters supporting the Donkey Party was found to be (0.41, 0.47).  A one-proportion z-test will be carried out, with hypotheses H₀:p = 0.50 and H_A:p not = 0.50. What decision can I make at  a level of significance of  0.05?

A one-proportion Z-test is being carried out, 1-tailed, with hypotheses H₀:p = 0.4 and H_A:p > 0.4.  A  z statistic of 1.83 has been calculated. Find the P-value, correct to three decimal places.

In a large class, the professor has each person toss a coin several times and calculate the proportion of his or her tosses that were heads.

The students then report their results, and the professor plots a histogram of these several proportions. The students toss the coin 80 times each, about 95% of all these samples should have sample proportions between what two numbers?

Use the 68-95-99.7 Rule to provide the appropriate response.

In a large class, the professor has each person toss a coin several times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions.

Use the 68-95-99.7 Rule to provide the appropriate response.

Consider a fair dice of 6 sides. The mean number on the face of a fair dice ( sampled many many times) has a distribution with mean 3.5 and standard deviation of 1.708 (correct to 3 decimal places).

If this was done many many times, what is the mean of the sampling distribution of all these sample averages?