Who uses instant messaging? Do younger people use online instant messaging (IM) more often than older people? A random sample of IM users found that of the people in the sample aged to said they used IM more often than email. In the to age group, of people used IM more often than email. Construct and interpret a % conﬁdence interval for the difference between the proportions of IM users in these age groups who use IM more often than email.
From the given information, it could be interpreted that there is the probability that the difference in the proportion of IM users lies between and
It is given in the question that,
The formula to compute the confidence interval for the difference in population proportion is :
The confidence interval using Ti- plus calculator is computed as:
Therefore, the confidence interval is ()
Therefore, it could be interpreted that there is probability that the difference in the proportion of IM users lies between and
School has students and School has students. A local newspaper wants to compare the distributions of SAT scores for the two schools. Which of he following would be the most useful for making this comparison?
(a) Back-to-back stemplots for A and B
(b) A scatterplot of A versus B
(c) Dotplots for A and B drawn on the same scale
(d) Two relative frequency histograms of A and B drawn on the same scale
(e) Two frequency histograms for A and B drawn on the same scale
Dropping out You have data from interviews with a random sample of students who failed to graduate from a particular college in years and also from a random sample of students who entered at the same time and did graduate. You will use these data to compare the percentages of students from rural backgrounds among dropouts and graduates.
A driving school wants to find out which of its two instructors is more effective at preparing students to pass the state’s driver’s license exam. An incoming class of students is randomly assigned to two groups, each of size . One group is taught by Instructor A; the other is taught by Instructor B. At the end of the course, of Instructor A’s students and of Instructor B’s students pass the state exam. Do these results give convincing evidence that Instructor A is more effective?
Min Jae carried out the significance test shown below to answer this question. Unfortunately, he made some mistakes along the way. Identify as many mistakes as you can, and tell how to correct each one.
State: I want to perform a test of
where the proportion of Instructor A's students that passed the state exam and the proportion of Instructor B's students that passed the state exam. Since no significance level was stated, I'll use
Plan: If conditions are met, I’ll do a two-sample test for comparing two proportions.
Random The data came from two random samples of students.
- Normal The counts of successes and failures in the two groups , and are all at least .
- Independent There are at least 1000 students who take this driving school's class.
Do: From the data, and . So the pooled proportion of successes is
- Test statistic
- -value From Table A, localid="1650450641188" .
Conclude: The -value, , is greater than , so we fail to reject the null hypothesis. There is no convincing evidence that Instructor A's pass rate is higher than Instructor B's.
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