Understanding Hypothesis Testing in Public Opinion Surveys

The video tutorial explains a public opinion survey on tax increase support, testing the null hypothesis that 50% of adults support it. A sample of 200 adults showed 56.5% support. The p-value of 0.033 is compared to significance levels to decide whether to reject the null hypothesis. The tutorial guides viewers through understanding p-values, significance levels, and making statistical decisions.

What was the main objective of the public opinion survey?

• To evaluate the effectiveness of tax policies.

• To assess the quality of the local school system.

• To find out the average income of adults.

• To determine if more than 50% of adults support a tax increase.

How many adults in the sample supported the tax increase?

• 87

• 113

• 150

• 200

What is the sample proportion of adults supporting the tax increase?

• 45.5%

• 50%

• 60%

• 56.5%

What does a p-value represent in hypothesis testing?

• The average value of the sample data.

• The proportion of the sample that supports the hypothesis.

• The probability of observing a result as extreme as the sample result, assuming the null hypothesis is true.

• The probability of the null hypothesis being true.

What is the significance level used to reject the null hypothesis?

• 0.01

• 0.50

• 0.05

• 0.10

If the p-value is less than the significance level, what should be concluded?

• The test is inconclusive.

• Fail to reject the null hypothesis.

• Reject the null hypothesis.

• Accept the null hypothesis.

At a significance level of 0.01, what conclusion can be drawn?

• More than 50% of adults support the tax increase.

• Less than 50% of adults support the tax increase.

• Exactly 50% of adults support the tax increase.

• The data is insufficient to draw a conclusion.

What happens if the p-value is greater than the significance level?

• Reject the null hypothesis.

• Fail to reject the null hypothesis.

• The test is invalid.

• Accept the alternative hypothesis.

What is the correct conclusion at a significance level of 0.05?

• More than 50% of adults support the tax increase.

• Less than 50% of adults support the tax increase.

• The null hypothesis is accepted.

• The test is inconclusive.

Which conclusion is incorrect at a significance level of 0.01?

• The null hypothesis is not rejected.

• The p-value is greater than the significance level.

• Conclude more than 50% support the tax increase.

• Fail to reject the null hypothesis.