Math Problem Statement

A newsletter publisher believes that more than 72% of their readers own a laptop. Is there sufficient evidence at the 0.05 level to substantiate the publisher's claim?

State the null and alternative hypotheses for the above scenario.

Solution

To evaluate the publisher's claim that more than 72% of their readers own a laptop, we need to formulate the null and alternative hypotheses as follows:

Null Hypothesis (H0H_0):

The proportion of readers who own a laptop is less than or equal to 72%. Mathematically: H0:p0.72H_0: p \leq 0.72

Alternative Hypothesis (HaH_a):

The proportion of readers who own a laptop is greater than 72%. Mathematically: Ha:p>0.72H_a: p > 0.72

This is a one-tailed test since the claim specifically states "more than 72%."

Would you like me to proceed with the test setup, calculations, or interpretation?

Related Questions:

  1. What test statistic should be used for this hypothesis test, and why?
  2. How do you calculate the p-value for this scenario?
  3. What would be the critical value for the 0.05 significance level in a one-tailed test?
  4. How does sample size affect the validity of this hypothesis test?
  5. What assumptions must be satisfied for this test to be reliable?

Tip: Always confirm the sample size and sample proportion to ensure the test is valid under the normal approximation!

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Proportions
Significance Levels

Formulas

Null Hypothesis: H0: p <= 0.72
Alternative Hypothesis: Ha: p > 0.72
Test Statistic: z = (p̂ - p) / √(p(1-p)/n)
P-value calculation based on the standard normal distribution

Theorems

Central Limit Theorem
Properties of the Normal Distribution

Suitable Grade Level

College Level or Advanced High School