Birthdays of hockey players: In Malcolm Gladwell’s book "Outliers" he shares the work of Canadian psychologist Roger Barnsley, who noticed that a disproportionately high percentage of elite ice-hockey players have birthdays between January and March. A group of statistics students would like to test if this is true for the Los Angeles Kings 2010-2015 rosters (22 out of 57). After debating whether this set of hockey players can be viewed as a random sample of hockey players, they decide to run a hypothesis test anyway to practice finding the P‐value. They test the hypotheses LaTeX: H_0H 0: LaTeX: p=0.25p = 0.25 versus LaTeX: H_aH a: LaTeX: p>0.25p > 0.25. They use a significance level of 0.05. Their calculated test statistic is 2.37. Using the applet (at the top of this Checkpoint), what is the P‐value?
a. P‐value = 0.009
b. P‐value = 0.991
c. P‐value = 0.018
d. P‐value = 0.05

The P-value is 0.009.

Step-by-step explanation:

We are given that after debating whether this set of hockey players can be viewed as a random sample of hockey players, they decide to run a hypothesis test anyway to practice finding the P‐value.

We are given that the following hypothesis below;

Null Hypothesis, : p = 0.25

Alternate Hypothesis, : p > 0.25

Now, the test statistics that was used here for the above hypothesis would be;  

                       T.S.  =    ~ N(0,1)

Also, the test statistics given to us is 2.37.

SO, the P-value of the test statistics is given by the following formula;

             P-value = P(Z > 2.37) = 1 - P(Z 2.37)

                           = 1 - 0.99111 = 0.00889 ≈ 0.009

The above probability is calculated by looking at the value of x = 2.37 in the z table which has an area of 0.99111.

Therefore, the required P-value is 0.009.

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'.

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step-by-step explanation: