Experiment 1:

A small ranching business would like to determine if the use of a new supplement will increase the weights of their adult cattle. A random sample of 40 cattle are given the supplement, with 19 showing an increase in weight. At the same time, a random sample of 34 cattle are selected as the control group, with 14 showing an increase in weight. Is there evidence at the 6% level of significance to suggest that the proportion of cattle that were given the supplement and showed an increase in weight is greater than the proportion of cattle from the control group that showed an increase in weight?

1. Let p₁ =

Let p₂ =

Ho:

Ha:

Excel Procedure:

1. In cell A1 through A8 type x1, x2, n1, n2, phat1, phat2, phat, and qhat.
2. In cell B1 through B4 enter the corresponding values for the variables in column A.
3. In cell B5 enter =B1/B3 and in cell B6 type =B2/B4.
4. In cell B7 enter =(B1+B2)/(B3+B4) and in cell B8 type =1-B7.
5. In cell D1 type "Z" and in cell D2 type "Area to the left of Z".
6. In cell E1 type =(B5-B6)/SQRT(B7*B8/B3+B7*B8/B4). This will calculate the test statistic Z for this hypothesis test.
7. Select cell E2, then Formulas (the tab at the top of the Excel window)->More Functions->Statistical->NORM.S.DIST.
8. When the Function Arguments window opens select (or enter) cell E1 for Z.
9. In the Cumulative field type TRUE. This gives the area to the left of Z in the standard normal curve.
10. Test Statistic: __________________
11. Area left of z: ___________
12. Adjust the area above to match the inequality in Ha in order to determine the p-value.

Hint: two-tail: pvalue = 2(left area), right tail: pvalue = 1- (left area), left tail: pvalue=left area

P-value: __________________

1. Conclusion (explain why using p-value method and interpret in context).

K7 III X V fx A B C D E F G H 1 x1 Z 2 X2 Area to the left of Z 3 n1 4 n2 5 phat1 6 phat2 7 phat 8 qhat 9 HO 11 12