Where’s Egypt? In a Pew Research poll, out of randomly selected U.S. men were able to identify Egypt when it was highlighted on a map of the Middle East. When randomly selected U.S. women were asked, were able to do so.
a. Construct and interpret a confidence interval for the difference in the true
proportion of U.S. men and U.S. women who can identify Egypt on a map.
b. Based on your interval, is there convincing evidence of a difference in the true
proportions of U.S. men and women who can identify Egypt on a map? Justify your
a. Confidence Interval is .
b. Yes, there is evidence of difference in true proportion of US men and women who can identify Egypt on map or not.
It is given that
The three conditions are:
Random: Samples are independent random samples.
Independent: US men are less than of population. Same is true for women.
Normal: Success in two samples are and failures are . All are greater than ten.
All conditions are satisfied.
The confidence interval is
As the confidence interval does not contain zero. It is unlikely that population proportions are equal.
So, there is evidence of difference in true proportion of US men and women who can identify Egypt on map or not.
Coaching and SAT scores Let’s first ask if students who are coached increased their scores significantly, on average.
a. You could use the information on the Coached line to carry out either a two-sample t test comparing Try 1 with Try 2 or a paired t test using Gain. Which is the correct test? Why?
b. Carry out the proper test. What do you conclude?
The distribution of grade point averages (GPAs) for a certain college is approximately Normal with a mean of and a standard deviation of The minimum possible GPA is 0.0 and the maximum possible GPA is . Any student with a GPA less than is put on probation, while any student with a GPA of 3.5 or higher is on the dean’s list. About what percent of students at the college are on probation or on the dean’s list?
Men versus women The National Assessment of Educational Progress (NAEP)
Young Adult Literacy Assessment Survey interviewed separate random samples of
men and women aged to years.
The mean and standard deviation of scores on the NAEP’s test of quantitative skills were x1= and s1= for the men in the sample. For the women, the results were x ̄2= and s2=.
a. Construct and interpret a % confidence interval for the difference in mean score for
male and female young adults.
b. Based only on the interval from part (a), is there convincing evidence of a difference
in mean score for male and female young adults?
Digital video disks A company that records and sells rewritable DVDs wants to compare the reliability of DVD fabricating machines produced by two different manufacturers. They randomly select DVDs produced by each fabricator and find that of the disks produced by the first machine are acceptable and of the disks produced by the second machine are acceptable. If are the proportions of acceptable DVDs produced by the first and second machines, respectively, check if the conditions for calculating a confidence interval for are met.
A random sample of size will be selected from a population, and the proportion of those in the sample who have a Facebook page will be calculated. How would the margin of error for a confidence interval be affected if the sample size were increased from to ?
(a) It remains the same.
(b) It is multiplied by .
(c) It is multiplied by .
(d) It is divided by .
(e) It is divided by .
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