10. Gay marriage In May 2012, a CNN/ORC Poll asked a random sample of 1009 U.S. adults this question: Do you think marriages between gay and lesbian couples should or should not be recognized by the law as valid, with the same rights as traditional marriages? Of those polled, 54% said they favored marriage equality, the highest percentage to date.
a) Create a 95% confidence interval for the percentage of all American adults who support marriage equality.
b) Based on your confidence interval, can you conclude that a majority of U.S. adults support legally recognizing gay marriages? Explain.
c) If pollsters wanted to follow up on this poll with another survey that could determine the level of support for gay marriage to within 2% with 98% confidence, how many people should they poll?
44. Batteries We work for the "Watchdog for the Consumer" consumer advocacy group. We've been asked to look at a battery company that claims its batteries last an average of 100 hours under normal use. There have been several complaints that the batteries don't last that long, so wedecide to test them. To do this we select 16 batteries and run them until they die. They lasted a mean of 97 hours, with a standard deviation of 12 hours.
a) One of the editors of our newsletter (who does not know statistics) says that 97 hours is a lot less than the advertised 100 hours, so we should reject the company's claim. Explain to him the problem with doing that.
b) What are the null and alternative hypotheses?
c) What assumptions must we make in order to proceed with inference?
d) At a 5% level of significance, what do you conclude? battery company that claims its batteries last an average
e) Suppose that, in fact, the average life of the of 100 hours under normal use. There have been several company's batteries is only 98 hours. Has an error complaints that the batteries don't last that long, so we been made in part d? If so, what kind?
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