Acertain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr. a random sample of 19 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data support the use of a one-sample t test. the relevant hypotheses are h0: μ = 10 versus ha: μ < 10. (a) if t = −2.5 and α = 0.05 is selected, what conclusion is appropriate? reject fail to reject (b) if t = −1.83 and α = 0.01 is selected, what conclusion is appropriate? reject fail to reject (c) if t = 0.57, what conclusion is appropriate? reject fail to reject

Fail to reject H0 in all three cases

Step-by-step explanation:

Given that a certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr.

(Right tailed test at 1% sign level)

n = 19

a) t =-2.5 , df = 18

p = 0.01154

p >1% hence Fail to reject H0

b) t = −1.83

p = 0.041931

p >1%  Fail to reject H0

c) t = 0.57

p = 0.287>1%  Fail to reject H0

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.