They decide to run the correct t-test with the results shown below.

t = 3.9246, df = 89, p-value = 0.0001708

Which of the following would you conclude based on this result?

Question

They decide to run the correct t-test with the results shown below.

t = 3.9246, df = 89, p-value = 0.0001708

Which of the following would you conclude based on this result?

BlackTom AI · Accepted Answer

A t-value of 3.9246 with p = 0.0001708 is strong evidence that the average number now is greater than before. 1) Relevant knowledge points and concepts - Null hypothesis (H0) typically: the mean number of patrons now equals the earlier mean (no change). - Alternative hypothesis (Ha) for a directional test: mean now > earlier mean (they serve more). - t-statistic sign indicates direction (positive means sample mean > hypothesized mean). - p-value gives probability of observing such an extreme t (or more) if H0 is true. Small p-values (< common α like 0.05) lead to rejecting H0. - Degrees of freedom (df = 89) determine critical t values but are not needed when p is given. 2) Step-by-step reasoning - Given t = 3.9246 (positive) and p = 0.0001708. - Compare p-value to a typical significance level α = 0.05: 0.0001708 << 0.05, so the result is statistically significant. - The positive t indicates the sample mean is larger than the comparison mean (direction = increase). 3) Intermediate calculations / comparisons - Two-sided critical t for df = 89 is about 1.987; observed t = 3.9246 > 1.987, so it lies in the rejection region for a two-sided α = 0.05 test. - If the test were one-sided, one-sided critical t ≈ 1.662; again 3.9246 > 1.662. Either way, the result is highly significant. - The tiny p-value (0.0001708) corresponds to a very low probability (~0.017%) of observing such a t under H0. 4) Why the correct answer is correct - Because p << 0.05, H0 is rejected. Because the t-statistic is positive, the sample evidence indicates an increase in average patrons. Thus the proper conclusion is that they serve significantly more patrons now. 5) Why other options are incorrect - "Significantly fewer" is wrong because t is positive (not negative). - "Significantly different but unknown direction" is wrong because the sign of t tells us the direction (increase). - "We cannot reject the null" is wrong because the p-value is far below conventional α levels, so we do reject H0. 6) Conclusion confirming the answer - Therefore, the correct conclusion is: On average, they serve significantly more patrons now. This matches the provided answer.

They decide to run the correct t-test with the results shown below. t = 3.9246, df = 89, p-value = 0.0001708 Which of the following would you conclude based on this result?Single choice

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