Volume task
A box 2 centimeters high, 3 centimeters wide, and 5 centimeters long can hold 40 grams of clay. A second box has twice the height, three times the width,
and the same length as the first box. How many grams of clay can it hold?

grams of clay it can hold = 6 × 40 = 240 grams

Step-by-step explanation:

The first box has a height 2 cm , width of 3 cm and a length of 5 cm. The box can only hold 40 grams of clay . The volume of the box can be calculated as follows

volume = length × width × height

height = 2 cm

width = 3 cm

length = 5 cm

volume = 5 × 3 × 2 = 30 cm³

The second box has twice the height of the first box , 3 times the width of the first box and retains the same length of the first box. The dimension are as follows

height = 2 × 2 = 4 cm

width = 3 × 3 = 9 cm

length = 5 cm

volume = length × width × height

volume = 5 × 9 × 4 = 180 cm³.

The volume of the second box is 6 times bigger than the first box therefore , it can hold 6 times the weight of the first box.

grams of clay it can hold = 6 × 40 = 240 grams

p value = 0.0174

Conclusion : we reject the null hypothesis

Step-by-step explanation:

Thinking step:

We need to perform a test to determine if the proportion of the good parts is the same for all three shifts at a significance level of

Assumption : all the population for each or the three shifts is not equal.

Calculation:

Let p₁ be the sample of the first shift

     p₂ be the sample of the second shift

     p₃ be the sample of the third shift

According to the null hypothesis

H₀ = p₁ = p₂ = p₃

In other words, all the population sample proportions are equal.

Alternatively, we can assume that the three shift are not equal p₁ ≠ p₂ ≠ p₃

Tabulating and performing the ² test gives 8.10

degrees of freedom:

df = k - 1

   = 3 - 1 = 2

Thus the degree of freedom is 2

Solving using the MINITAB software gives: p = 0.174

The solution shows that the p value < level of significance, then p-value lies in the range 0.0174≤≤0.05

Therefore, we reject the null hypothesis based on the fact that the three shifts are not equal.