Question

The COVER paint company claims that a new accelerator added to latex paint will decrease the drying time by 4%. One of their salesmen has done his own testing and believes that the additive will decrease drying time by even more than 4%. His testing results are as listed in the attachment (numbers are percentages, i.e. 5.20 = 5.20%). Find x-bar rounded correctly to 2 decimal places. 5.20 6.40 3.80 6.30 4.70 5.40 3.20 4.70

A. 4.99

B. 4.94

C. 4.98

D. 4.96

E. 4.97

F. 4.95

Part b find the standard deviation Sx of the sample correctly rounded to 2 decimal places

A. 1.24

B. 1.25

C. 1.12

D. 1.13

E. 1.14

F. 1.26

Part c , what is the null hypothesis

A. H_o: μ = 4.0

B. H_o: μ = 5.2

C. H_o: μ = 4.96

D. H_o: μ = 6

E. H_o: μ = 1.24

F. H_o: μ = 1.12

Part d, what is alternative hypothesis H_a?

A. H_a: μ > 4

B. H_a: μ < 4

C. H_a: μ ≠ 4

D. H_a: μ < 4.96

E. H_a: μ > 4.96

F. H_a: μ ≠ 4.96

Part e, is this a t* or z* statistic?

A. t*

B. z*

C. neither

D. both

Part f, if it is t*, what is the degree of freedom?

A. It is z*

B. 6

C. 7

D. 8

E. 9

F. 10

Part g, what is the value of the test statistic?

A. 2.19

B. 2.40

C. 2.27

D. it cannot be determined

E. 2.32

F. 2.52

Part h,between what 2 p-values does the test statistic lie?

A. .05 and .04

B. .01 and .005

C. .04 and .02

D. .025 and .02

E. .10 and .05

F. .02 and .01

Answer 1

Data from the testing result (X values) :-

5.20 , 6.40 , 3.80 , 6.30 , 4.70 , 5.40 , 3.20 , 4.70

n = 8 (number of observations in the data)

Let   denote the i th value of X

Part a

To find x-bar which is the sample mean () we use the formula

Answer of the part a :   D. 4.96

Part b

To find the sample standard deviation () we use the formula

Answer of the part b : C. 1.12

Part c

Null hypothesis :

: = 4.0

Answer of the part c : A.   : = 4.0

Part d

Alternative hypothesis :

: > 4.0

Answer of the part d : A.   : > 4.0

Part e

It is a test as population standard deviation is not given

Answer of the part e : A.  

Part f

Degrees of freedom = (n-1) = (8-1) = 7

Answer of the part f : C. 7