Question

90 percent confidence interval for the proportion difference p1−p2 was calculated to be (0.247,0.325). Which of the following conclusions is supported by the interval?


A. There is evidence to conclude that p1>p2 because 0.325 is greater than 0.247.
B. There is evidence to conclude that p1 C.There is evidence to conclude that p1>p2 because all values in the interval are positive.
D. There is evidence to conclude that p1 E. There is evidence to conclude that p2>p1 because 0.247 and 0.325 are both greater than 0.05.

Answer 1

Answer:

C

Step-by-step explanation:

Statistics!!

When we have a confidence interval for the difference in proportions or means, our null hypothesis is always that there's no difference. (H0 = p1-p2 = 0.)

If the difference is positive, that means we have sufficient evidence p1>p2.

If it's negative, then we have sufficient evidence p2>p1.

Why not A: incorrect interpretation of the interval

Why not B: doesn't look like a complete answer

Why not D: also doesn't look like a complete answer

Why not E: this confuses the definition of alpha-level and p-value with confidence interval values. If those were p-values and greater or less than an alpha-level, we would reject or fail to reject the null hypothesis. That isn't the case here.

Answer 2

You can use the fact that the 90% confidence interval given is all positive value for the test statistic being the difference of $p_1$ and $p_2$.

The conclusion that is supported by the given confidence interval is given by:

Option C: There is evidence to conclude that $p_1 > p_2$ because all values in the interval are positive.

How can we conclude that there is evidence that  $p_1 > p_2$?

Since it is given that the difference is measured by $p_1 - p_2$,

and  since the given confidence interval at 90% confidence for that difference is obtained to be (0.247,0.325), thus we can say that 90% difference value of   $p_1 - p_2$, will be lying in that given interval.

Since the interval is all positive, thus we can say that 90% of the times, the difference  $p_1 - p_2$ will be positive which indicates that $p_1 > p_2$

Thus, the conclusion that is supported by the interval is given by:

Option C: There is evidence to conclude that $p_1 > p_2$ because all values in the interval are positive.

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