Question

In an article in the Journal of Advertising, Weinberger and Spotts compare the use of humor in television ads in the United States and in the United Kingdom. Suppose that independent random samples of television ads are taken in the two countries. A random sample of 400 television ads in the United Kingdom reveals that 141 use humor, while a random sample of 500 television ads in the United States reveals that 122 use humor.

(a) Set up the null and alternative hypotheses needed to determine whether the proportion of ads using humor in the United Kingdom differs from the proportion of ads using humor in the United States.

H₀: p₁ ? p₂ (Click to select)≠= 0 versus H_a: p₁ ? p₂ (Click to select)≠= 0.

(b) Test the hypotheses you set up in part a by using critical values and by setting ? equal to .10, .05, .01, and .001. How much evidence is there that the proportions of U.K. and U.S. ads using humor are different? (Round the proportion values to 3 decimal places. Round your answer to 2 decimal places.)

  z           

(Click to select)RejectDo not Reject H₀ at each value of ?; (Click to select)extremely strongstrongvery strongnonesome evidence.

(c) Set up the hypotheses needed to attempt to establish that the difference between the proportions of U.K. and U.S. ads using humor is more than .05 (five percentage points). Test these hypotheses by using a p-value and by setting a equal to .10, .05, .01, and .001. How much evidence is there that the difference between the proportions exceeds .05? (Round the proportion values to 3 decimal places. Round your z value to 2 decimal places and p-value to 4 decimal places.)

z
p-value

(Click to select)RejectDo not Reject H₀ at each value of ? = .10 and ? = .05; (Click to select)nonevery strongextremely strongstrongsome evidence.

(d) Calculate a 95 percent confidence interval for the difference between the proportion of U.K. ads using humor and the proportion of U.S. ads using humor. Interpret this interval. Can we be 95 percent confident that the proportion of U.K. ads using humor is greater than the proportion of U.S. ads using humor? (Round the proportion values to 3 decimal places. Round your answers to 4 decimal places.)

95% of Confidence Interval                      [ , ]

(Click to select)YesNo the entire interval is above zero.

Answer 1

a)

null Hypothesis:    Ho:    p1-p2		=	0.00
alternate Hypothesis: Ha:   p1-p2		≠	0.00

b)

z =3.57

p value =0.0004

Reject H₀ at each value of alpha ; extremely strong evidence

c)

test stat z=(p̂1-p̂2)/Se =		1.93
P value   =		0.0268

reject Ho at each value of 0.10 and 0.05

strong evidence

d)

for 95 % CI value of z=		1.96
margin of error E=z*std error =		0.0602
lower bound=(p̂1-p̂2)-E=		0.0488
Upper bound=(p̂1-p̂2)+E=		0.1692

95% Ci =0.0488 , 0.1692

Yes the entire interval is above zero.