The following n = 10 observations are a sample from a normal population. 7.4 7.0 6.5 7.4 7.6 6.2 6.9 7.6 6.5 6.9 (a) find the mean and standard deviation of these data. (round your standard deviation to four decimal places.) mean standard deviation (b) test h0: μ = 7.5 versus ha: μ < 7.5. use α = 0.01. test statistic: t =

Mean, x:7

standard deviation(s)=0.4944

t=-3.1980

Step-by-step explanation:

given data

7.4 7.0 6.5 7.4 7.6 6.2 6.9 7.6 6.5 6.9

Count, N:10

Sum, Σx:70

Mean, x:7

Variance, s2:  0.24444444444444

Steps  

s2 =

     =

     =  

     =0.24444444444444

s =  

⇒s= 0.49441323247304

⇒s=0.4944

b) H0: μ = 7.5 versus Ha: μ < 7.5.

   α = 0.01.

    t=

    t=

    t=-3.1980

for 9 df and α = 0.01

t stat from table is -2.82

as t test is less than t

we reject the null hypothesis

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )

$2416.6

step-by-step explanation:

per hour = $ 25

total work time = 35

commission = 15%

total she has to make = $ 4,500

let she sold x dollar products

so her commission will be 15 % of x

now

total = weekly basic pay + commission

4500= (25*35) + 15 % of x

4500=875 + * x

4500-875 =   * x

3625= * x

multiplying wwith 100 on both sides gives

36250 = 15 x

now

x =  

x= $2416.6