Wally Watchmaker is interested in determining the preferences for digital vs analog watches. He samples 200...

Wally Watchmaker is interested in determining the preferences for digital vs analog watches. He samples 200 individuals and asks them their age and their preference. Test at an α = .05 to determine if age and watch preferences are independent of each other

Age	Digital	Analog	Undecided
Younger than 30	90	40	10
Older than 30	10	40	10

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Expert Solution

Wally Watchmaker is interested in determining the preferences for digital vs analog watches. He samples 200 individuals and asks them their age and their preference. We are to test at an α = .05 to determine if age and watch preferences are independent of each other.

For this we apply chi-square test of independence between the variables.

We are to test,

H₀: Age & watch preferences are independent of each other vs. H₁: Age & watch preferences are dependent

The test-statistic is:

The observed frequencies are tabulated as:

OBSERVED
Age	Digital	Analog	Undecided	Marginal
Younger than 30	90	40	10	140
Older than 30	10	40	10	60
Marginal	100	80	20	200

The expected frequencies are tabulated as:

OBSERVED
Age	Digital	Analog	Undecided
Younger than 30	70	56	14
Older than 30	30	24	6

Where, Expected frequency of a cell= (Row total * Column total)/Total frequency

degrees of freedom for the test statistic= (No. of rows)*(No. of columns)-1= (3-1)*(2-1)= 2

Given, level of significance= = 0.05

Clearly, 39.0959(observed)>5.991(tabulated or expected,as obtained from Values of chi-square table)

So, according to the sample we can conclude that, age & watch preferences are strongly related/dependent to each other.

orchestra answered 1 year ago

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