Q1. Is the majority of consumers uncomfortable with drone deliveries? (Given: 1009 surveyed, 545 said "no")

Background

Topic: Hypothesis Testing for a Population Proportion

This question tests your ability to set up and conduct a hypothesis test for a population proportion, using sample data to determine if there is significant evidence to support a claim about the population.

Key Terms and Formulas

• Null Hypothesis (H0): The statement that the population proportion equals a specific value.

• Alternative Hypothesis (H1): The statement that the population proportion differs from the value in H0 (here, greater than 0.5).

• Test Statistic (z):

• Where:

  • = sample proportion

  • = hypothesized population proportion

  • = sample size

• P-value: The probability of obtaining a test statistic as extreme as the observed one, assuming H0 is true.

Step-by-Step Guidance

1. Express the claim in symbolic form. Here, the claim is that the majority are uncomfortable: .

2. State the null and alternative hypotheses:

   • Null hypothesis:

   • Alternative hypothesis:

3. Check requirements for using the normal approximation:

   • Sample is random

   • Both and (with , , )

4. Calculate the sample proportion:

5. Calculate the test statistic using the formula:

Try solving on your own before revealing the answer!

Q2. Find the value of the test statistic for the claim: Most adults do not have hypertension. (n = 988, 71.1% do not have hypertension)

Background

Topic: Hypothesis Testing for a Population Proportion

This question asks you to calculate the test statistic for a claim about a population proportion, using sample data.

Key Terms and Formulas

• Test Statistic (z):

• Where:

  • = sample proportion

  • = hypothesized population proportion

  • = sample size

Step-by-Step Guidance

1. Express the claim in symbolic form. "Most" means .

2. Calculate the sample proportion: (since 71.1% of 988 adults do not have hypertension).

3. Set the null hypothesis: and alternative hypothesis: .

4. Calculate .

5. Plug the values into the test statistic formula:

Try solving on your own before revealing the answer!

Q3. Find the value of the test statistic for the claim: The mean pulse rate of adult males is equal to 70 bpm. (n = 151, sample mean = 67.7 bpm, s = 11.1 bpm)

Background

Topic: Hypothesis Testing for a Population Mean (σ unknown)

This question tests your ability to calculate the test statistic for a sample mean when the population standard deviation is not known.

Key Terms and Formulas

• Test Statistic (t):

• Where:

  • = sample mean

  • = hypothesized population mean

  • = sample standard deviation

  • = sample size

Step-by-Step Guidance

1. Express the claim in symbolic form: bpm.

2. Calculate the sample mean bpm and sample standard deviation bpm.

3. Set the null hypothesis: and alternative hypothesis: .

4. Plug the values into the test statistic formula:

Try solving on your own before revealing the answer!