In a quality control test of parts manufactured at Dabco Corporation, an engineer sampled parts produced on the first, second, and third shifts. The research study was designed to determine if the population proportion of good parts was the same for all three shifts. Sample data follow.

Production Shift

Quality first second third

Good 285 368 176

Defective 15 32 24

A. Using a .05 level of significance, conduct a hypothesis test to determine if the population proportion of good parts is the same for all three shifts. What is the p-value and what is your conclusion?

B. If the conclusion is that the population proportions are not all equal, use a multiple comparison procedure to determine how the shifts differ in terms of quality. What shift or shifts need to improve the quality of parts produced?

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.

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: