Two machines used to fill soft drink containers are being compared. The number of containers filled each minute is counted for 60 minutes for each machine. During the 60 minutes, machine 1 filled an average of 73.8 cans per minute with a standard deviation of 5.2 cans per minute, and machine 2 filled an avaerage of 76.1 cans per minute with a standard deviation of 4.1 cans per minute. Required:
a. If the counts are made each minute for 60 consecutiveminutes, what assumption necessary to the validity of a hypothesistest may be violated?
b. Assuming that all necessary assumptions are met, perform a hypothesis test. Can you conclude that machine 2 is faster than machine 1?

The calculated value |t| = |  - 2.6932 | = 2.6932 > 1.9803 at 0.05 level of significance

Alternative hypothesis is accepted

The average of machine two is faster than machine one

Step-by-step explanation:

Step(i):-

Given sample size  n₁ = n₂ = 60 minutes

The average of first sample 'x⁻₁ = 73.8

The standard deviation of the first sample 'S₁ ' = 5.2 cans per minute

The average of second sample 'x⁻₂ = 76.1

The standard deviation of the second sample 'S₂ ' =  4.1 cans per minute

step(ii):-

Null Hypothesis : H₀: 'x⁻₁ = 'x⁻₂

Alternative Hypothesis : H₁ :  'x⁻₁ > 'x⁻₂

Test statistic

       t =  - 2.6932

|t| = |  - 2.6932 | = 2.6932

Step(iii):-

Degrees of freedom

ν = n₁ + n₂ -2 = 60 +60 -2 = 118

t₀.₀₅ = 1.9803

The calculated value |t| = |  - 2.6932 | = 2.6932 > 1.9803 at 0.05 level of significance

Final answer:-

Null hypothesis is rejected  at  0.05 level of significance

Alternative hypothesis is accepted

The average of machine two is faster than the average of machine one

450 is the final answer! : )

step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

hope this : )