State the hypothesis and claim: The expense of moving the storage yard for the consolidated Package Delivery Service is justified only if it can be shown that the daily average travel distance is less than 214 mi. In 12 trial runs the average distance was 198 mi with a standard deviation of 42 mi At a = .01 test the claim that the average daily travel distance is less than 214 mi.

the claim is . H0: ___ H1:

Null Hypothesis: H₀ : μ < 214 miles

Alternative Hypothesis :H₁: μ> 214 miles

The calculated value |t| = 1.319 < 3.4966 at 0.01 level of significance

Null hypothesis is accepted

The average daily travel distance is less than 214 miles

Step-by-step explanation:

Step(i):-

Given that the size of the sample 'n' = 12

The mean of the Population = 214 miles

The mean of the sample   = 198 miles

The standard deviation of the sample = 42 miles

Level of significance = 0.01

Step(ii):-

Null Hypothesis: H₀ : μ < 214 miles

Alternative Hypothesis :H₁: μ> 214 miles

Test statistic

          |t| = |- 1.319| = 1.319

Degrees of freedom   = n-1 = 12 -1 =11

critical value  

The calculated value |t| = 1.319 < 3.4966 at 0.01 level of significance

Null hypothesis is accepted

The average daily travel distance is less than 214 miles

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

The answer is in the image 

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

The answer is in the image 

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Given height of gymnasium is 5/6 height of 30 foot ball

therefore height of gymnasium=5/6 * 30

=25 feet