In this problem, we're going to be testing the effectiveness off seat bells we have to simple random samples off to groups off people. The first group is off. People not wearing seatbelts on the second group is for people who are wearing seatbelts, and we have proportions off people who, um, were killed during a car crash. So P one represents the portion off people who were killed on not wearing seatbelts, and that is that you won out off 2823 and P two. Heart represents the proportion off people who were killed in a car crash. Yet they were wearing seatbelts, and that is 16 out of 7000 765. So in the in this problem, you're going to be testing the the clean that seat belts are effective introducing fatalities, and the first step would be testing the claim using hypothesis test. So, for the hypothesis, the null hypothesis behalf p one equals P two, and for the alternative hypotheses we have P one is greater than P two. This implies that not wearing, uh, does the proportion of people who are killed when they are not wearing seatbelts is much higher than the proportion of people who were killed when they are wearing signals. That means that, uh, the seat belts are effective introducing fatalities. So for the test statistic, we need to substitute the values that you just obtained here into the formula. And when we do that, the value off the calculated value of that is 6.49 Okay. And since this is a one tailed test, the critical value is going to be 1.645 at 0.1 level 0.5 level of significance. Now we can compare these two values off that for the critical value, we can shade from 1.645 on the right and we can see that 6.45 is greater than 6.49 is greater than 1.6 now 45 which means that our calculated value is with being the critical region. And for that reason we conclude that we need to reject the nal hypotheses. And by rejecting the null hypothesis, we conclude that there is sufficient evidence to support the claim that the fatality rate is higher for those not wearing seatbelts. Next, we're going to test the claim by constructing on ah confidence interval and in this case we're going to construct a 90% confidence interval and fast. We need to get the margin of error e by using the formula given. And once we do that, the value off E is 0.33 We then need to substitute it to subtract it to the difference, be one heart and be too hot, and then added the difference to create the range. So in this case, the off the fast part will be p one minutes p two hut minus e and that gives you 0.57 now should be less than P one minus p two. And that is less than than when the some off the difference be one hut on and be may not speak to heart plus e which is 0.123 So we notice that the confidence interval limits do not include zero. And that means that the two fatality rates are not equal. Uh huh. And since the confidence interval limits on Lee include positive values, we can conclude that the fatality rate is higher for those not wearing seat bells. So once again, the claim has Bean supported using that the confidence interval method. Next, we're going to give an explanation to what the results suggest about the effectiveness off seat bells. So as we have seen, the proportions are different, and even when we check the proportions will notice that he won are divided by 202,828 gives us 1.1% and never on the P P. Two hot gives us 0.2%. And as you can see, the fast proportion is much greater. It's significantly larger, 1.1% is significantly larger than 0.2%. So the results suggest that the use of seat belt is associate it with fatalities, um, fatality rates that are lower than those as she waited with no, not using seat belts. So if you're using seatbelt, you're much more secure than when you're not