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Chapter 8: Q. 16 (page 483)

Many teens have posted profiles on sites such as Facebook and My Space. A sample survey asked random samples of teens with online profiles if they included false information in their profiles. Of 170younger teens (ages 12to 14) polled, 117said 鈥淵es.鈥� Of 317older teens (ages 15to 17) polled, 152 said 鈥淵es.鈥�6 A 95% confidence interval for the difference in the population proportions (younger teens 鈥� older teens) is 0.120 to 0.297. Interpret the confidence interval and the confidence level

Short Answer

Expert verified

Interpretation confidence level: The confidence interval contains the true difference in population proportions, on average, in 95%of all samples.

Step by step solution

01

Given Information

A sample survey asked random samples of teens with online profiles if they included false information in their profiles.

02

Explanation

The given 95%confidence interval for the difference in population proportions is 0.120to 0.297.

Interpretation: We are 95%confidence that the difference in the population proportions between younger teens and older teens is between 0.120and 0.297.

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Most popular questions from this chapter

School vouchers A national opinion poll found that 44% of all American adults agree that parents should be given vouchers that are good for education at any public or private school of their choice. The result was based on a small sample.

(a) How large an SRS is required to obtain a margin of error of 0.03(that is, 卤3%) in a 99% con铿乨ence interval? Answer this question using the previous poll鈥檚 result as the guessed value for p鈭�.

(b) Answer the question in part (a) again, but this time use the conservative guess p鈭�=0.5. By how much do the two sample sizes differ?

33. Going to the prom Tonya wants to estimate what proportion of her school鈥檚 seniors plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to the prom.
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(b) Check conditions for constructing a confidence interval for the parameter.

(c) Construct a 90% confidence interval for p. Show your method.
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To assess the accuracy of a laboratory scale, a standard weight known to weigh 10grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is 10grams if the scale has no bias). In previous studies, the standard deviation of the scale readings has been about 0.0002gram. How many measurements must be averaged to get a margin of error of 0.0001with 98% confidence? Show your work.

Going to the prom Tonya wants to estimate what proportion of the seniors in her school plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to the prom

You have an SRS of 23 observations from a Normally distributed population. What critical value would you use to obtain a 98% confidence interval for the mean M of the population if S is unknown?

(a) 2.508

(b) 2.500

(c) 2.326

(d) 2.183

(e) 2.177
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