Question

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 283 American trade magazine advertisements, 59 were humorous. An independent random sample of 198 British trade magazines contained 28 humorous ads.

(1)	State the decision rule for .10 significance level: H0: πA = πB; H1: πA ≠ πB. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Reject H0 if z <  or z >

(2)	Compute the value of the test statistic. (Do not round the intermediate values. Negative values should be indicated by a minus sign. Round your answer to 2 decimal places.)

Value of the test statistic

(3)	Does this data provide evidence that there is a difference in the proportion of humorous ads in British versus American trade magazines? Use the .10 significance level.

(Reject, Do not reject) H0. There is (insufficient, sufficient) evidence to indicate that there is a difference in the proportion of humorous ads in British versus American trade magazines.

Answer 1

1)

The z value at 90% confidence interval is,

alpha = 1 - 0.90 = 0.1
alpha/2 = 0.1/2 = 0.05
Zalpha/2 = Z0.05 = 1.64

Reject H0 if z < -1.64 0r z > 1.64

2)

p1 = 28/198 = 0.1414

p2 = 59/283 = 0.2479

pcap = (p1*n1+p2*n2)/(n1+n2)
= ( 0.1414 * 198 + 0.2479 * 283)/(198 + 283)
= 0.1995

z = (p1 - p2)/srqt(pcap *(1-pcap) *(1/n1+1/n2))
= ( 0.1414 - 0.2479)/sqrt(0.1995 *(1-0.1995) *(1/198 + 1/283))
= -2.88

3)

Reject H0 There si sufficient evidence to indicate that there is a difference in the proportion of humorous ads in British versus American trade magazines.