For x1=34,n1=50,x2=52,&n2=75x_1=34,n_1=50,x_2=52,\&n_2=75, test the claim that p1<p2p_1<p_2 for α=0.01\alpha=0.01 using ...(B) Confidence Interval

C-level = 0.99, not enough evidence to suggest p 1 < p 2 p_1<p_2 .

For x 1 = 34 , n 1 = 50 , x 2 = 52 , & n 2 = 75 x_1=34,n_1=50,x_2=52,\&n_2=75 , test the claim that p 1 < p 2 p_1<p_2 for α = 0.01 \alpha=0.01 using ... (B) Confidence Interval

Welcome back. For this problem, we have the same values for x one, n one, x two, and n two, and we still wanna test the claim that p one is less than p two for alpha equals 0.01. But this time, we wanna do it using a confidence interval. As a reminder, the confidence interval will be for the difference between the two proportions, so p one minus p two. Now if it is true that p one is less than p two, then that would mean that p one minus p two would be negative because a smaller number minus a larger number is negative. So if our confidence interval only included negative values, that would be enough evidence to suggest that p one is less than p two. So we'll be paying attention to whether our confidence interval is entirely negative or whether it includes zero and some positives. So let's make that confidence interval. We'll start by clicking on the stat button, scrolling to the right to the test menu, and we want option b, so let's scroll down to it. Once there, we can click enter, and that's step one all set. You'll notice that the values we've already entered in for x one, n one, x two, and n two are already there, so that's all set. We will need to adjust our confidence level or c level. As a reminder, alpha is 0.01, and our c level is going to be one minus our alpha value, which in this case is one minus point zero one, which is point nine nine. So we should change that point nine five to a point nine nine. Once that's all set, we can scroll down to calculate and click enter. That's step two, all set. And we'll see our confidence interval appear in the viewing window. It goes from approximately negative 0.23 to about 0.21. Now I can see here that this is not just negatives. It goes from a negative to a positive. So this confidence interval includes positives and zero. This means that we do not have enough evidence. To suggest that p one is less than p two. Great work.

For x 1 = 34 , n 1 = 50 , x 2 = 52 , & n 2 = 75 x_1=34,n_1=50,x_2=52,\&n_2=75 , test the claim that p 1 < p 2 p_1<p_2 for α = 0.01 \alpha=0.01 using ... (B) Confidence Interval

C-level = 0.99, not enough evidence to suggest p 1 < p 2 p_1<p_2 .

C-level = 1, we reject the H 0 H_0 since there is enough evidence to suggest p 1 < p 2 p_1<p_2 .

C-level = 0.99, we fail to reject the H 0 H_0 H 0

10. Hypothesis Testing for Two Samples

Two Proportions

Statistics

10. Hypothesis Testing for Two Samples

Two Proportions

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Multiple Choice

For $x_{1} = 34, n_{1} = 50, x_{2} = 52, & n_{2} = 75$ , test the claim that $p sub 1 is less than p sub 2$ for $alpha equals 0.01$ using ...
(B) Confidence Interval

C-level = 0.99, not enough evidence to suggest $p sub 1 is less than p sub 2$ .

C-level = 1, we reject the $H sub 0$ since there is enough evidence to suggest $p sub 1 is less than p sub 2$ .

C-level = 0.99, we fail to reject the $H_0$

The confidence interval does not include zero, we fail to reject $H sub 0$ .

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