Question

The University of Illinois decided to conduct a study at their university. The 90% confidence interval for the true difference in proportions between undergraduates and graduates is (−0.0119, 0.1885). Without doing any calculations, what can you say about the p-value of a TWO-SIDED test? Circle the best correct answer.

Group of answer choices

a. p-value > 0.10

b. p-value = 0.10

c. p-value < 0.10

d. There is not enough information to tell.

Answer 1

Ans:

Because the confidence intervals contain The null hypothesis i.e H0:p1-p2=0 .

Therefore we accept null hypothesis .

If p value >0.1 then we accept null hypothesis

a) P value >0. 10

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Answer 2

1. Key Concept:

• A 90% confidence interval for a two-sided test corresponds to testing at the 10% significance level ($\alpha =0.10$).

• The interval $(-0.0119,0.1885)$ includes zero (the null value for no difference in proportions).

• 
  

2. Relationship Between CI and $p$-value:

• If a 90% CI includes zero, the two-sided $p$-value must be > 0.10.

• If the CI excluded zero, the $p$-value would be < 0.10.

• 
  

3. Why Not Other Options?

• b. $p$-value = 0.10: Only true if the CI endpoint exactly touches zero (not here).

• c. $p$-value < 0.10: Requires the CI to exclude zero.

• d. Not enough info: False; the CI directly answers this.

• 
  

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Answer:

a. $p$-value > 0.10