Question 14 (1 point) Saved The government wants to clamp...

Question 14 (1 point) Saved The government wants to clamp down on the use of a particular pesticide X in crop- growing. They suggest that a maximum value of 0.05 ppm should be found when crops are screened for this pesticide. A random sample of of crops were selected to test for the level of this pesticide. The sample information is summarized below: n = 150, $\bar{y}$ = 0.036 ppm, s = 0.001 ppm Find the upper bound of the 95% confidence interval for the amount of pesticide present in the crops sampled [Note: For n = 150 and this level of significance, the critical value is t* = 1.976] Note: 1- Round your intermediate numbers to 4 decimal places. 2- Round you final answer to 3 decimal places. Enter your final answer to 3 decimal places. Your Answer: 0.036

Transcript

00:01 All right, so we're looking at a family that owns a large grape vineyard, and they are testing two new insecticides, pronode 5 and action.

00:13 And these are the number of vines checked, and this is the number of infested vines.

00:20 After these vines were sprayed with these insecticides.

00:26 And what we're going to do is test at the alpha of 0 .10 level of significance if there's a difference in the proportion of vines so we're looking at there's a difference that means and the hypothesis is that p1 is equal to p2 and we're going to call per node 5 we're going to call that group 1 and actually we'll call that group 2 are the proportions the same against the alternative not equal are they different significantly different from each other we're tested at this alpha level.

00:56 And that means we're going to do a two -proportion z -test.

01:00 And if our p -value is less than the alpha value, if this is less than that, we're going to reject our hypothesis.

01:10 This is our rejection rule here.

01:12 And we're going to get that p -value from a z -statistic for a difference of proportions.

01:23 And we could also use a critical value.

01:36 The critical value approach, you could use the p -value approach or the critical value approach and we'll do both because they're they're both nice to nice to see so this is one rule if the p value is the alpha there's another that if your z statistic is greater than this critical value a pen is acting up on me there we go if your z value is there you go greater than your z critical value and since it's a two -tail test we'll do absolute value, then you will reject.

02:19 And so let's get that value.

02:28 So if you were to look up 0 .01 in your alpha table, or a z -table, you would find it would go along with the 1 .28.

02:42 But that's not it.

02:43 We need to actually think of this as a two -tailed test, where you have some lower, so negative z critical value and some positive z critical value such that the error to the right here is 0 .05 and the error to the left is also 0 .05 and these two add up to 0 .1 this critical value is 1 .64 and if it's down here it's negative but that's why we do the absolute value so often and you might see is 1 .645 so the the absolute value of 1 .645 is our z statistic greater than that value.

03:28 All right, let's go and get our z statistic, and we'll wrap this up.

03:31 So this is done by taking the p -hat estimate for p -hat 1 minus p -hat 2 divided by the square root of the pooled proportion p -hat times 1 minus p -hat times 1 over the sample size of group 1 plus 1 over the sample size of group 2.

03:51 All right, let me make that n look better for us.

03:54 And this one.

03:56 That's our formula...

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