Anutritionist claims that the mean tuna consumption by a person is 3.5 pounds per year. a sample of 70 people shows that the mean tuna consumption by a person is 3.3 pounds per year. assume the population standard deviation is 1.22 pounds. at alphaequals0.02, can you reject the claim?

Let μ = mean tuna consumption (in pounds per year)

H0: μ = 3.1

HA: μ ≠ 3.1

Sample mean = 2.9

Standard deviation = 0.94

Standard error of mean = s / √ n

Standard error of mean = 0.94 / √ 60

SE = 0.94/7.746

Standard error of mean 0.1214

z = (xbar- μ ) / SE

z = (2.9-3.1) / 0.1214

z = -1.6481

p-value = P( z < -1.6481)+P( z > 1.6481) = 2 (0.0495) = 0.099

Fail to reject null hypothesis since 0.099 >0.08

The nutritionist's claim that the mean tuna consumption by a person in the U.S is 3.1 pounds per year is not rejected.

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