Aresearcher drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 209 times. the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6 respectively are 36, 30, 41, 40, 23, and 39. use a 0.05 significance level to test the claim that the outcomes are not equally likely. does it appear that the loaded die behaves differently than a fair die?

Step-by-step explanation:

Given that the observed frequencies for the outcomes as follows:

To check this we can use chi square goodness of fit test.

(Two tailed test at 5% significance level)

Assuming equally likely expected observations are found out and then chi square is calculated as (0-E)^2/E

Df = 6-1 =5

OutcomeFrequencyExpected frequency(Obs-exp)^2/Exp

13634.833333330.03907496

23034.833333330.670653907

34134.833333331.091706539

44034.833333330.766347687

52334.833333334.019936204

63934.833333330.498405104

209209          7.086124402

p value =0.214

Since p >alpha, we accept null hypothesis

It appears that the  loaded die does not behave differently than a fair die at 5% level of significance

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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step-by-step explanation: