A marketing research firm suspects that a particular product has higher name recognition among college graduates than among high school graduates. A sample from each population is selected, and each asked if they have heard of the product in question. A summary of the sample sizes and number of each group answering “yes” are given below:
College Grads (Pop. 1):High School Grads (Pop. 2):n1=99,n2=100,x1=71,x2=51
Is there evidence, at an ?=0.073 level of significance, to support the claim of higher name recognition among college graduates? Carry out an appropriate hypothesis test, filling in the information requested.
A. The value of the standardized test statistic:
B. The p-value is
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Question 2
Two random samples are taken, one from among first-year UVA students and the other from among fourth-year UVA students. Both samples are asked if they favor modifying the Honor Code. A summary of the sample sizes and number of each group answering “yes” are given below:
First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=86,n2=93,x1=41,x2=61
Is there evidence, at an ?=0.07 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested.
A. The value of the standardized test statistic:
B. The p-value is
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Question 3
Two random samples are taken, one from among UVA students and the other from among UNC students. Both groups are asked if academics are their top priority. A summary of the sample sizes and proportions of each group answering “yes” are given below:
UVA (Pop. 1):UNC (Pop. 2):n1=90, n2=81, pˆ1=0.758 pˆ2=0.685
Find a 96.4% confidence interval for the difference p1?p2 of the population proportions.
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