10.1
What are the two conditions that need to be satisfied in order to construct a confidence interval for p1-p2?
The random and the large counts conditions
What do you use to calculate the standard error of the sampling distribution of p1-p2?
p-hat combined
hatp_c
True/False: A confidence interval for p1-p2 provides convincing evidence for a difference of proportions when the interval contains 0.
False. If 0 is contained in the interval, it is plausible that there is no difference.
True/False: When experimenters use volunteers as subjects, researchers should not generalize the results of an experiment beyond individuals like the ones in the experiment.
The book and movie A Civil Action, tells the story of a major legal battle that took place in the small town of Woburn, Massachusetts. A town well that supplied water to East Woburn residents was contaminated by industrial chemicals. During the period that residents drank water from this well, 16 of the 414 babies born had birth defects. On the west side of Woburn, 3 of the 228 babies born had birth defects. Let p1 = the proportion of all babies born with birth defects in West Woburn and p2 = the proportion of all babies born with birth defects in East Woburn. Check if the conditions for calculating a confidence interval for p1-p2 are met.
Random? Not a random sample, the data include the whole population
LCC? 16, 398, 3 and 225 are not all ≥ 10
Does the order in which options are presented influence people's responses? Eric randomly assigned 100 people to one of two groups. He asked the first group, "Which southwestern restaurant chain do you like better Chipotle or Qdoba?" He asked the second group, "Which southwestern restaurant chain do you like better Qdoba or Chipotle?" In the "Chipotle first" group, 31 of the 50 people said they preferred Chipotle. In the "Qdoba first" group, 25 of the 50 people said they preferred Chipotle. State the appropriate hypotheses for performing a significance test. Be sure to define the parameter.
H0: p1 - p2 = 0, p1=p2
Ha: p1 - p2 ≠ 0, p1≠p2
p1 - p2 is the true difference in proportions of people who said they preferred Chipotle ("Chipotle first" - "Qdoba first")
A sample survey was given to separate SRSs of 500 high school students and 550 college students. Researchers want to determine whether there is a difference in the proportion of high school and college students who are employed. In all, 20.4% of the high school students and 45.1% of the college students are employed. Let p1 = the proportion of high school students who are employed and p2 = the proportion of college students who are employed. Calculate a 99% confidence interval for the difference (High school - college) in the true proportion of students who are employed. Based on the interval, is there convincing evidence that a lesser proportion of high school students are employed than college students?
-0.319 to -0.175
Yes, all of the values of the interval are negative.
Does the order in which options are presented influence people's responses? Eric randomly assigned 100 people to one of two groups. He asked the first group, "Which southwestern restaurant chain do you like better Chipotle or Qdoba?" He asked the second group, "Which southwestern restaurant chain do you like better Qdoba or Chipotle?" In the "Chipotle first" group, 31 of the 50 people said they preferred Chipotle. In the "Qdoba first" group, 25 of the 50 people said they preferred Chipotle. Calculate the test statistic and find the P-value.
z = 1.21
P-value = 2(0.1131) = 0.2262