For each of these problems follow the 6-step Hypothesis Testing Guideline on Sli

Question

For each of these problems follow the 6-step Hypothesis Testing Guideline on Slide 4 of the CH 11 Power Point. You can use the p-value or the critical value method. You can calculate the test statistic and p-value (Step 4) either by hand using the formulas and tables, with a graphing calculator, or by using StatCrunch. Include the details of your calculations, not just the values. If you use the critical value method, state the critical value instead of the p-value. Remember to include the Expected value for a GOF test or the Expected matrix for a Chi-square test.

1) A company says its premium mixture of nuts contains 10% Brazil nuts, 20% cashews, 20% almonds, and 10% hazelnuts, and the rest peanuts. You buy a can and separate the various kinds of nuts. Upon counting them, you find there are 27 Brazil nuts, 44 cashews, 49 almonds, 17 hazelnuts, and 108 peanuts. Is your mix significantly different from what the company advertises?

2) The table below shows the ranks attained by male and female officers in the New York City Police Department (NYPD). Does these data indicate that men and women are equitably represented at all levels of the department?

                      Male     Female

Officer:        21,900   4,281

Detective:    4,058    806

Sergeant:    3,898    415

Lieutenant: 1,333 89

Captain       359      12

Higher Ranks: 218 10

Explanation / Answer

1)

for above p value = 0.3951 which is greater then 0.05 level ; hence we can not reject null hypothesis that mix has same proportion  what the company advertises

2)

p value for above test stat 0.201 and 5 degree of freedom =0.0000 wehich is less then 0.05 level hence we reject null hypothesis and conclude that data indicate that men and women are not equitably represented at all levels of the department

observed Expected Chi square type Probability O E=total*p =(O-E)^2/E Brazil nuts 0.100 27.000 24.50 0.26 cashew 0.200 44.000 49.00 0.51 almonds 0.200 49.000 49.00 0.00 hazelnuts 0.100 17.000 24.50 2.30 peanuts 0.400 108.000 98.00 1.02 1 245 245 4.0816

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