A study was conducted to determine if there was a difference

A study was conducted to determine if there was a difference in the humor content in British and American trade magazine advertisements. In an independent random sample of 277 American trade magazine advertisements, 64 were humorous. An independent random sample of 201 British trade magazines contained 35 humorous ads.

State the decision rule for .05 significance level: H₀: ?_A = ?_B; H₁: ?_A ? ?_B. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)

Compute the value of the test statistic. (Do not round the intermediate values. Round your answer to 2 decimal places.)

Does this data provide evidence that there is a difference in the proportion of humorous ads in British versus American trade magazines? Use the .05 significance level.

(Click to select)Fail to rejectRejectH₀. There is (Click to select)no significanta significantdifference in the proportion of humorous ads in British versus American trade magazines.

Solution

(1) Given a=0.05, the critical values are Z(0.025) =-1.96 or 1.96 (from standard normal table)

Reject H₀ if z < -1.96 or z >1.96

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(2)test statistic:

p1=64/277=0.2310469

p2=35/201= 0.1741294

Z=(p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.2310469-0.1741294)/sqrt(0.2310469*(1-0.2310469)/277+0.1741294*(1-0.1741294)/201)

=1.55

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(3) Fail to reject Ho

There is no significanta difference in the proportion of humorous ads in British versus American trade magazines.