Question

1. a report claims that 38% of adults own more than one car. upon surveying a random sample of adults, a researcher finds that 33% of the adults in the sample own more than one car. when a hypothesis test is conducted based on this sample of data, it is reported that the results are statistically significant. what does this mean?

a. the difference between 33% and 38% is large enough to be meaningful in practical terms.
b. the observed result provides evidence against the null hypothesis.
c. if we assume the null hypothesis is true, the observed difference would occur just by chance about 1 in 20 times.
d. the null hypothesis is false and the true parameter is 33%.
e. the researcher has proven that fewer than 38% of all adults own more than one car.

Explanation:

• Option A: Statistical significance is not about practical - meaningfulness in terms of the size of the difference. It is about the probability of observing the result under the null hypothesis.
• Option B: Statistical significance means that the observed result (in this case, the sample proportion of \(33\%\) when the claim is \(38\%\)) is unlikely to have occurred if the null hypothesis (usually \(H_0:p = 0.38\)) is true. So, it provides evidence against the null hypothesis.
• Option C: If the significance level \(\alpha=0.05\) (which is common, and a \(1\) in \(20\) chance), statistical significance just means that the \(p -\)value is less than \(\alpha\). But the statement in option C is not the general definition of statistical significance. Statistical significance is about the \(p -\)value being less than the significance level, not specifically about a \(1\) in \(20\) chance (unless \(\alpha = 0.05\)).
• Option D: Statistical significance does not prove that the null hypothesis is false and that the sample proportion is the true population proportion. It just gives evidence against the null hypothesis.
• Option E: Hypothesis testing does not "prove" a claim. It provides evidence for or against a claim.

Answer:

B. The observed result provides evidence against the null hypothesis.