6.26 The Daily Show: A 2010 Pew Research foundation poll indicates that among 1,099 college graduates, 33% watch The Daily Show. Meanwhile, 22% of the 1,110 people with a high school degree but no college degree in the poll watch The Daily Show. A 95% confidence interval for (pcollege grad - ?pHS or less), where p is the proportion of those who watch The Daily Show, is (0.07, 0.15). Based on this information, determine if the following statements are true or false, and explain your reasoning if you identify the statement as false. (data:dailyShow) (a) At the 5% significance level, the data provide convincing evidence of a difference between the proportions of college graduates and those with a high school degree or less who watch The Daily Show. ( ) true ( ) false (b) We are 95% confident that 7% less to 15% more college graduates watch The Daily Show than those with a high school degree or less. ( ) true ( ) false (c) 95% of random samples of 1,099 college graduates and 1,110 people with a high school degree or less will yield differences in sample proportions between 7% and 15%. ( ) false ( ) true
6.26 The Daily Show: A 2010 Pew Research foundation poll indicates that among 1,099 college graduates, 33% watch The Daily Show. Meanwhile, 22% of the 1,110 people with a high school degree but no college degree in the poll watch The Daily Show.
A 95% confidence interval for (pcollege grad - ?pHS or less), where p is the proportion of those who watch The Daily Show, is (0.07, 0.15). Based on this information, determine if the following statements are true or false, and explain your reasoning if you identify the statement as false. (data:dailyShow)
(a) At the 5% significance level, the data provide convincing evidence of a difference between the proportions of college graduates and those with a high school degree or less who watch The Daily Show.
( ) true
( ) false
(b) We are 95% confident that 7% less to 15% more college graduates watch The Daily Show than those with a high school degree or less.
( ) true
( ) false
(c) 95% of random samples of 1,099 college graduates and 1,110 people with a high school degree or less will yield differences in sample proportions between 7% and 15%.
( ) false
( ) true
Given:
The total number of college graduates are n=1099.
The proportion of college graduates who watch the daily show is 0.33.
The total number of high school graduates are m=1110.
The proportion of high school graduates who watch the daily show is 0.22.
The 95% confidence interval (C.I) for the difference of proportion of college graduates and those with a high school degree or less who watch The Daily Show is given as:
(a)
In the given scenario, it can be observed that the confidence interval does not contain the null value, this implies that the null hypothesis is rejected and there is a significant difference between the proportion of college graduates and those with a high school degree or less who watch The Daily Show.
Hence, the given statement is true at 5% level of significance.
Thus, the answer is true.
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