Can any sample proportion less than 0.5 be used to support a claim that the population proportion is greater than 0.5?

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based on a random sample of 640 college students, the mean amount of sleep college students. construct a 95% confidence interval for the mean amount of sleep per night for college studenrs.

To determine whether a sample proportion can be used to support a claim about the population proportion, we need to perform a hypothesis test. The hypothesis test involves setting up null and alternative hypotheses and examining the sample data to make an inference about the population parameter.

In this case, the claim is that the population proportion is greater than 0.5. To set up the null and alternative hypotheses:

Null hypothesis (H0): The population proportion is less than or equal to 0.5.
Alternative hypothesis (Ha): The population proportion is greater than 0.5.

To conduct the hypothesis test, we usually use a significance level (α) to define the threshold for rejecting the null hypothesis. Commonly, α is set to 0.05. If the p-value calculated from the sample data is smaller than α, we reject the null hypothesis in favor of the alternative hypothesis.

Now, to answer the question specifically about sample proportions less than 0.5, it is possible for a sample proportion less than 0.5 to support the claim that the population proportion is greater than 0.5. However, the strength of the evidence depends on the sample size and the difference between the sample proportion and the hypothesized population proportion.

If the sample size is large and the sample proportion is reasonably close to 0.5, there is a greater chance of rejecting the null hypothesis and supporting the claim of a population proportion greater than 0.5. On the other hand, if the sample size is small, the evidence might not be strong enough to support the claim.

In summary, a sample proportion less than 0.5 can be used to support a claim that the population proportion is greater than 0.5, but the strength of the evidence depends on various factors like sample size and the difference between the sample proportion and the hypothesized population proportion. Performing a hypothesis test is crucial to make a valid inference.