An inspector inspects a shipment of medications to determine the efficacy in terms of the proportion p in the shipment that failed to retain full potency after 60 days of production. Unless there is clear evidence that this proportion is less than 0.05, she will reject the shipment. To reach a decision, she will test the following hypotheses using the large-sample test for a population proportion: H0 : p = 0.05, Ha : p < 0.05
To do so, she selects an SRS of 200 pills. Suppose that eight of the pills have failed to retain their full potency. The proportion 'p-hat' for the proportion of pills that have failed to retain their potency is:.

Solution :

It is given that :

    (Null hypothesis, is also correct)

    (Alternate hypothesis, also called )

This is a lower tailed test,

Therefore,

Sample proportion,

                                    = 0.04

And claimed proportion, P = 0.05

Significance level, = 0.01

Therefore, calculating the statistics, we get

Standard deviation of

Test statistic,

Now since this is a lower tailed test, p-value =

Rejection Criteria : Reject if p-value < α .

Conclusion : Since the p-value , we fail to reject the null hypothesis. There is insufficient evidence that p is less than 0.05

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.