For a random sample of Harvard University psychology majors, the responses on political ideology had a mean of 3.18 and standard deviation of 1.72 for 51 nonvegetarian students and a mean of 2.22 and standard deviation of .67 for the 20 vegetarian students. When we use software to compare the means with a significance test, we obtain the following printout. Variances T DF Prob>|T|Unequal 2.9146 41.9 0.006Interpret the P-value, in context, based on its definition.

From the test give in the question it is obvious that  there is enough evidence to show that population mean varies for vegetarian and non-vegetarian

The P-value helps affirm the null hypothesis claims,The P-value attains  values relatively as large as that which exists in the sample given,if the null hypothesis is right

Step-by-step explanation:

From the question we are told that

Sample mean

Standard deviation

Sample size

Sample mean

Standard deviation

Sample size

Generally this is a two tailed test

therefore

   Null hypothesis  =

  Alternative hypothesis

From the test give in the question it is obvious that  there is enough evidence to show that population mean varies for vegetarian and non-vegetarian

The P-value helps affirm the null hypothesis claims,The P-value attains  values relatively as large as that which exists in the sample given,if the null hypothesis is right

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180