In an article in the Journal of Advertising, Weinberger and Spotts compare the u
ID: 3261542 • Letter: I
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 146 use humor, while a random sample of 500 television ads in the United States reveals that 125 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. H_0: p_1? p_2 0 versus H_a: p_1? p_2 (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.) H_0 at each value of ?: 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.) H_0 at each value of ? = 10 and? = 05 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 the entire interval is above zero.Explanation / Answer
Answer:
a).
H_0: P_1 - P_2 =0 H_1: P_1 - P_2 eq 0
b).
z=3.74
Reject Ho at all the levels : 0.1, 0.05, 0.01, 0.001. There is significant evidence.
Z Test for Differences in Two Proportions
Data
Hypothesized Difference
0
Level of Significance
0.05
Group 1
Number of Items of Interest
146
Sample Size
400
Group 2
Number of Items of Interest
125
Sample Size
500
Intermediate Calculations
Group 1 Proportion
0.365
Group 2 Proportion
0.25
Difference in Two Proportions
0.115
Average Proportion
0.3011
Z Test Statistic
3.7370
c).
z=2.11
P=0.0173
Reject Ho at 0.10 and 0.05 level. There is significant evidence.
Z Test for Differences in Two Proportions
Data
Hypothesized Difference
0.05
Level of Significance
0.05
Group 1
Number of Items of Interest
146
Sample Size
400
Group 2
Number of Items of Interest
125
Sample Size
500
Intermediate Calculations
Group 1 Proportion
0.365
Group 2 Proportion
0.25
Difference in Two Proportions
0.115
Average Proportion
0.3011
Z Test Statistic
2.1122
Upper-Tail Test
Upper Critical Value
1.6449
p-Value
0.0173
d).
95% CI for difference = (0.0544, 0.1756)
Yes, the entire interval is above zero.
Z Test for Differences in Two Proportions
Data
Hypothesized Difference
0
Level of Significance
0.05
Group 1
Number of Items of Interest
146
Sample Size
400
Group 2
Number of Items of Interest
125
Sample Size
500
Intermediate Calculations
Group 1 Proportion
0.365
Group 2 Proportion
0.25
Difference in Two Proportions
0.115
Average Proportion
0.3011
Z Test Statistic
3.7370
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