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Chi-square test: Cockpit Noise & Colors of M&M candies

1. High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this hazard for many hours. A Boeing 727 co-pilot collected 61 noise observations using a handheld sound meter. Noise level is defined as "Low" (under 88 decibels), "Medium" (88 to 91 decibels), or "High" (92 decibels or more). There are three flight phases (Climb, Cruise, Descent). Research question: At α = .05, is the cockpit noise level independent of flight phase?
Be sure to test whether the Chi-Square table has too many cells with expected value less than 5. If it does, then combine the Cruise and Descent columns and try again.
Observed frequencies
Noise Level Climb Cruise Descent Row Total
Low 6 2 6 14
Medium 18 3 8 29
High 1 3 14 18
Col Total 25 8 28 61
Step 1: State the null and alternate hypotheses

Step 2: Select a level of significance
α = 0.05

Step 3: Identify the test statistic and state its formula

Step 4: Formulate a decision rule

Step 5: Make a decision
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2. In 1995, with the introduction of the color blue in M&M candy bags, a researcher purchased several bags and counted the number of each color present. The results are given in the table below. Perform a goodness of fit test to determine, at the 0.1 significance level, what can be said about whether the colors were equally distributed in the overall population of M&M candies.
Observed frequencies
Red 73
Green 41
Blue 69
Brown 78
Yellow 62
Orange 58
Sum = 381
Step 1: State the null and alternate hypotheses

Step 2: Select a level of significance
α = 0.1

Step 3: Identify the test statistic and state its formula

Step: 4 Formulate a decision rule

Step 5: Make a decision

See attached file.

Need solutions to steps 1-5 for the 2 attached questions.

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Solution Summary

The solution provides step by step method for the calculation of chi square test for association. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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