3.55 What Proportion Believe in One True Love? In Data 2.1 on page 46, we descri

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3.55 What Proportion Believe in One True Love? In Data 2.1 on page 46, we describe a study in which a random sample of 2625 US adults were asked whether they agree or disagree that there is "only one true love for each person." The study tells us that 735 of those polled said they agree with for the mean response time for game players minus the mean response time for non-players is -1.2 seconds, while a 95% confidence interval for mean accuracy score for game players minus mean accuracy scor (a for non-players is -4.2 to +5.8. nterpret the meaning of the 95% confidence the statement. The standard error for this sample proportion is 0.009. Define the parameter estimated, give the best point estimate, the margin interval for difference in mean response time (b) Is it likely that game players and non-game players are basically the same in response time? Why or why not? If not, which group is faster of error, and find and interpret a 95% confidence interval. 3.56 Males vs Females and One True Love In Data 2.1 on page 46, we describe a study in which a random sample of 2625 US adults were asked (with a smaller response time)? (c) Interpret the meaning of the 95% confidence interval for difference in mean accuracy score. whether they agree or disagree that there is only(d) Is it likely that game players and non-game play- one true love for each person." The response and gender of the participants is shown in Table 3.6. Use the information in the table to construct and interpret a 95% confidence interval for the differ- ence in the proportion who agree, between males ers are basically the same in accuracy? Why or why not? If not, which group is more accurate? 3.58 Bisphenol A in Your Soup Cans Bisphenol A (BPA) is in the lining of most canned goods, and recent studies have shown a and females, using the fact that the standard error between BPA exposure and behavior and health for the difference is 0.018. Is it plausible that there problems. How much does canned soup consurm is no difference between males and females in the inary BPA concentration? That was proportion who agree that each person has only one the question addressed in a recent study in which consumption of canned soup over five days was asso- ciated with a more than 1000% increase in urinary tion increase ur true love? Table 3.6 Is there only one true love for each BPA. In the study, 75 participants ate either canne soup or fresh soup for lunch for five days. On the fifth day, urinary BPA levels were measured. After a two-day break, the participants switched group and repeated the process. The difference in BPA levels between the two treatments was measured for each participant. The study reports that a 95% con fidence interval for the difference in means (canne Agree Disagree 363 34 78 2625 minus fresh) is 19.6 to 25.5 g/L, ) Is this a randomized comparative experiment 3.57 Playing Video Games A new study provides some evidence that playing action video games strengthens a person's ability to translate sen (b) What parameter are we estimating? sory information quickly into accurate decisions. (c) Interpret the confidence interval in terms Researchers had 23 male volunteers with an aver or a matched pairs experiment? Why might th type of experiment have been used BPA concentrations age age of 20 look at moving arrays on a computer screen and indicate the direction in which the dots were moving26 Half of the volunteers (11 men) reported playing action video games at least f times a week for the previous year, while the other 3.59 Predicting Election Results Throughout th 12 reported no video game playing in the previ ous year. The response time and the accuracy score updates on the sample proportion su were both measured. A 95% confidence interval (d) If the study had included 500 participant instead of 75, would you expect the confidenc interval to be wider or narrower? US presidential election of 2012, polls gave regula

Explanation / Answer

3.55

sample size = n = 2625

sample proportion = p = 735/2625 = 0.28

standard error of proportion = se = 0.009

Here we have estimated the sample propotion and we want to know about the parameter "Population proportion" that is the proportion of US adults that think that there is one true love for each person

95% confidence interval = p +- Zcritical * se

= 0.28 +- 1.96 * 0.009

= (0.2624, 0.2976)

Here 95% confidence intervalmeans that there is 95% probability that from a random sample size of given, there is 26.24% to 29.76% chance that US adults agree that there is one love for each person.

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