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.
You can use the fact that the 90% confidence interval given is all positive value for the test statistic being the difference of [tex]p_1[/tex] and [tex]p_2[/tex].
The conclusion that is supported by the given confidence interval is given by:
Option C: There is evidence to conclude that [tex]p_1 > p_2[/tex] because all values in the interval are positive.
Since it is given that the difference is measured by [tex]p_1 - p_2[/tex],
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 [tex]p_1 - p_2[/tex], will be lying in that given interval.
Since the interval is all positive, thus we can say that 90% of the times, the difference [tex]p_1 - p_2[/tex] will be positive which indicates that [tex]p_1 > p_2[/tex]
Thus, the conclusion that is supported by the interval is given by:
Option C: There is evidence to conclude that [tex]p_1 > p_2[/tex] because all values in the interval are positive.
Learn more about confidence interval here:
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