To determine if there is sufficient evidence to substantiate the publisher's claim, we need to set up the null and alternative hypotheses. The hypotheses are based on the population proportion $p$ of readers who own a personal computer.

Null Hypothesis ($H_0$):

The null hypothesis assumes that the proportion of readers who own a personal computer is equal to or less than 43% ($p = 0.43$).

$H_0: p \leq 0.43$

Alternative Hypothesis ($H_a$):

The alternative hypothesis is the claim the publisher wants to support: that the proportion of readers who own a personal computer is greater than 43% ($p > 0.43$).

$H_a: p > 0.43$

This is a one-tailed test since the alternative hypothesis specifies a direction ($p > 0.43$).

Would you like me to proceed with further steps, such as calculating the test statistic, critical value, or p-value?

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5 Related Questions:

1. What sample size and data (e.g., the number of readers surveyed and how many own a computer) are required to test this hypothesis?
2. How do you determine the critical value for a one-tailed hypothesis test at the 0.05 level of significance?
3. What is the formula for calculating the test statistic for a population proportion?
4. How does the decision rule (rejecting or failing to reject $H_0$) depend on the p-value?
5. What is the practical interpretation of rejecting $H_0$ in the context of this problem?

Tip:

For hypothesis testing involving proportions, always ensure your sample size is large enough to satisfy the conditions for normal approximation ($np \geq 10$ and $n(1-p) \geq 10$).