1. A market researcher wanted to determine whether the proportion of beer drinke

Question

1. A market researcher wanted to determine whether the proportion of beer drinkers who preferred Peroni increased as a result of an advertising campaign. A random sample of 1,200 beer drinkers was selected. The results indicating preference for Peroni or Maretti prior to the beginning of the advertising campaign and after its completion are shown in the table above.

a). At the .04 level of significance, is there evidence that the proportion of beer drinkers who prefer Peroni is lower at the beginning of the advertising campaign than at the end of the advertising campaign. Explain whether or not the advertising campaign was worth it. Please show work.

Preference After Completion of the Advertising Campaign Preference Prior to Advertising Campaign Peroni 606 132 738 Maretti 54 408 462 Total 660 540 1200 Peroni Maretti Tuial

Explanation / Answer

Solution

Let p1 and p2 be the proportion of all beer drinkers who prefer Peroni before and after the compaign respectively.

Claim:

Proportion of beer drinkers who prefer Peroni is lower at the beginning of the advertising campaign than at the end of the advertising campaign, i.e., p1 < p2

Hypotheses:

Null: H0 : p1 = p2 Vs Alternative: HA : p1 < p2

Test Statistic:

Z = (p1cap - p2cap)/{pcap(1 - pcap){(2/n)}, where

p1cap = proportion of beer drinkers who prefer Peroni in the sample at the beginning

p2cap) = proportion of beer drinkers who prefer Peroni in the sample at the end

n = total number of beer drinkers covered by the survey

pcap = (p1cap + p2cap)/2

Calculations:

Now, from the given data, out of 1200 beer drinkers, 660 prefer Peroni at the beginning, and out of 1200 beer drinkers, 738 prefer Peroni at the end.

Hence, p1cap = 660/1200 = 0.55, p2cap = 738/1200 = 0.615,

p1cap = (0.55 + 0.615)/2 = 0.5825 and

Z = (0.55 – 0.615)/ {(0.5825 x 0.4175)(2/1200)} = - 0.065/0.0004053229   

   = = - 0.065/0.0201 = - 3.2286.

Distribution and p-value:

Under H0, Z ~ N(0, 1) and so, p-value = P(Z < -3.2286) = 0.0006[using Excel Function]

Level of Significance () and Rejection Region:

Given = 0.04, H0 is rejected since p-value <

Conclusion:

There is evidence to support the claim that the proportion of beer drinkers who prefer Peroni is lower at the beginning of the advertising campaign than at the end of the advertising campaign and hence the advertising campaign was worth it.

DONE

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