A newsletter publisher believes that over $$ 50 \% $$ of their readers own a laptop. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.01 level of significance, the advertiser decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim?

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In hypothesis testing, we typically start with a null hypothesis ($$H_0$$) and an alternative hypothesis ($$H_a$$). In this case, the hypotheses can be defined as follows:

- $$H_0$$: The proportion of readers who own a laptop is $$50\%$$ or less ($$p \leq 0.5$$).
- $$H_a$$: The proportion of readers who own a laptop is greater than $$50\%$$ ($$p > 0.5$$).

The advertiser is testing this claim at a significance level of $$0.01$$. When the advertiser decides to reject the null hypothesis, it means that the evidence from the sample data is strong enough to conclude that the proportion of readers who own a laptop is greater than $$50\%$$.

Since the null hypothesis has been rejected, the conclusion is that there is sufficient evidence to support the publisher's claim that more than $$50\%$$ of their readers own a laptop. Thus, the advertiser can reasonably conclude that the publisher's claim is valid based on the results of the hypothesis test.
The advertiser rejected the null hypothesis, indicating that there is strong evidence to support the publisher's claim that over $$50\%$$ of their readers own a laptop.

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