Aresearch report claims that 20% of all individuals use firefox to browse the web. a software company is trying to determine if the proportion of their users who use firefox is significantly different from 0.2. in a sample of 200 of their users, 36 users stated that they used firefox. using this data, conduct the appropriate hypothesis test using a 0.01 level of significance. a) what are the appropriate hypotheses?
a)h0: p = 0.2 versus ha: p < 0.2
b)h0: p = 0.2 versus ha: p ≠ 0.2
c)h0: μ = 0.2 versus ha: μ > 0.2
d)h0: p = 0.2 versus ha: p > 0.2
b) what is the test statistic?
give your answer to four decimal places.
c) what is the p-value for the test? give your answer to four decimal places.
d) what is the appropriate conclusion?
a)fail to reject the claim that the firefox proportion is 0.2 because the p-value is smaller than 0.01.
b)conclude that the firefox proportion is not 0.2 because the p-value is smaller than 0.01.

(a) H0: p = 0.2 versus Ha: p ≠ 0.2

               (b) The test statistics is z- statistics = - 0.7071

               (c) The P - value = 0.4796

               (d) Conclude that the Firefox proportion is  0.2 because the P-value          is larger than 0.01.

Step-by-step explanation: The test is a 2 - sided test , using the Z- statistics:

Sample mean = 36/200 = 0.18

Population mean = 0.2

Therefore:

Z =

=

= - 0.7071

Therefore , the test statistics = - 0.7071

(c) The P - value for the 2 - sided test implies

2 * P ( Z > /-0.7071/ ) = 0.4796

(d) Conclude that the Firefox proportion is 0.2 because the P- Value is larger than 0.01

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

asdsaddsa

step-by-step explanation: