A 94% confidence interval for β0 is given by ( 10 , 15.1 ).

Is is possible that β0 = 24.751?

Enter 1 if it is possible.

Enter 0 if it is not possible.

c004.p0430.q001

Question

A 94% confidence interval for β0   is given by ( 10 , 15.1 ).

Is is possible that β0  = 24.751?

Enter 1 if it is possible.

Enter 0 if it is not possible.

c004.p0430.q001

BlackTom AI · Accepted Answer

A 94% confidence interval (10, 15.1) indicates the set of values that are plausible for β0 at the 94% confidence level; values inside the interval are consistent with the data, values outside are not.

Step-by-step reasoning:
1. Relevant concepts:
   - A (1 − α)% confidence interval gives a range of parameter values that would not be rejected by a two-sided hypothesis test at significance level α. Here 1 − α = 0.94, so α = 0.06.
   - If a candidate value lies inside the confidence interval, it is consistent with the data at that confidence level; if it lies outside, the data provide evidence against that value at the corresponding α.
2. Compare the candidate value to the interval endpoints:
   - Lower bound = 10
   - Upper bound = 15.1
   - Candidate β0 = 24.751
   - Since 24.751 > 15.1, it lies to the right of the upper bound.
3. Intermediate steps / calculation:
   - 24.751 − 15.1 = 9.651, so the candidate exceeds the upper bound by 9.651 units.
   - Because it is outside the interval, it would be rejected by the corresponding two-sided test at α = 0.06.
4. Why the correct answer is correct:
   - The confidence interval summarizes plausible values; 24.751 is not within the plausible range (10, 15.1), so it is not possible (i.e., not plausible at the 94% confidence level) that β0 = 24.751.
5. Why the alternative is incorrect:
   - Entering 1 would claim the value is possible (plausible). That contradicts the interval, because the value is outside the interval and therefore inconsistent with the data at the 94% confidence level.
6. Conclusion:
   - The correct response is 0 (not possible). This matches the conclusion above.

A 94% confidence interval for β0 is given by ( 10 , 15.1 ). Is is possible that β0 = 24.751? Enter 1 if it is possible. Enter 0 if it is not possible. c004.p0430.q001简答题

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