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Statistics Questions from Nov 23,2024

Browse the Statistics Q&A Archive for Nov 23,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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In a recent poll, the Gallup Organization found that \( 45 \% \) of adult Americans believe that the overall state of moral values in the United States is poor. If a survey of a random sample of 20 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral values, complete parts (a) through ( g ) below. (a) Explain why this is a binomial experiment. Select all that apply. 12 \( \square \) A. The probability of success is the same for each trial of the experiment. \( \square \) B. The trials are independent. \( \square \) C. The experiment is performed a foxed number of times. \( \square \) D. There are two mutually exclusive outcomes, success or failure. \( \square \) E. The probability of success is different for each trial of the experiment. \( \square \) F. Each trial depends on the previous trial. \( \square \) G. There are three mutually exclusive possible outcomes, arriving on-time, arriving early, and arriving late. \( \square \) H. The experiment is performed until a desired number of successes are reached. Use the following information: \[ \begin{array}{l}x_{1}=18, n_{1}=46, x_{2}=32, n_{2}=83 \\ \text { and the formula to compute the pooled proportion: } \\ \qquad \widehat{p}_{p}=\frac{x_{1}+x_{2}}{n_{1}+n_{2}}=\square \\ \quad \text { (Round the answer to } 4 \text { decimals) }\end{array} \text {. } \] According to a survey, \( 27 \% \) of residents of a country 25 years old or older had eamed at least a bachelor's degree. You are performing a study and would like at least 10 people in the study to have earned at least a bachelor's degree. (a) How many residents of the country 25 years old or older do you expect to randomly select? (b) How many residents of the country 25 years old or older do you have to randomly select to have a probability 0.989 that the sample contains at least 10 who have earned at least a bachelor's degree? (a) The number of randomly selected residents is (Round up to the nearest integer.) (c) Would it be unusual to observe 170 smokers who started smoking before turning 18 years old in a random sample of 200 adult smokers? A. Yes, because 170 is greater than \( \mu+2 \sigma \). B. Yes, because 170 is between \( \mu-20 \) and \( \mu+2 \alpha \) C. No, because 170 is less than \( \mu-2 \alpha \) D. Yes, because 170 is between \( \mu-20 \) and \( \mu+2 \sigma \). E. No, because 170 is between \( \mu-2 \sigma \) and \( \mu+2 \sigma \). According to an almanac, \( 80 \% \) of adull smokers started smoking before turning 18 years old. (a) Compute the mean and standard deviation of the random variable \( X \), the number of smokers who started before 18 in 200 trials of the probability experiment. (b) Interpret the mean. (c) Would it be unusual to observe 170 smokers who started smoking before turning 18 years old in a random sample of 200 adult smokers? Why? (a) \( \mathrm{p}_{\mathrm{x}}=160 \) \( \sigma_{\mathrm{x}}=5.7 \) (Round to the nearest tenth às needed.) (b) What is the correct interpretation of the mean? A. It is expected that in a random sample of 200 adult smokers, 160 will have started smoking before furning 18 . B. It is expected that in \( 50 \% \) of random samples of 200 adult smokers, 160 will have started smoking before turning 18 . C. It is expected that in a random sample of 200 adult smokers, 160 will have started smoking after turning 18 . St According to an almanac, \( 80 \% \) of adult smokers started smoking before turning 18 years old. (a) Compute the mean and standard deviation of the random variable \( X \), the number of smokers who started before 18 in 200 trials of the probability experiment. (b) Interpret the mean. (c) Would it be unusual to observe 170 smokers who started smoking before turning 18 years old in a random sample of 200 adult smokers? Why? 1 \( \sigma_{x}=\square \) (Round to the nearest tenth as needed.) (a) \( \mu_{\mathrm{x}}=160 \) 16 According to an almanac, \( 80 \% \) of adult smokers started smoking before turning 18 years old. (a) Compute the mean and standard deviation of the random variable \( X \), the number of smokers who started before 18 in 200 trials of the probability experiment. (b) Interpret the mean. (c) Would it be unusual to observe 170 smokers who started smoking before turning 18 years old in a random sample of 200 adult smokers? Why? (a) \( \mu_{\mathrm{x}}=\square \) According to an almanac, \( 80 \% \) of adult smokers started smoking before turning 18 years old. (a) Compute the mean and standard deviation of the random variable \( X \), the number of smokers who started before 18 in 100 trials of the probability experiment. (b) Interpret the mean. (c) Would it be unusual to observe 85 smokers who started smoking before turning 18 years old in a random sample of 100 adult smokers? Why? (a) \( \mu_{\mathrm{x}}= \) According to an almanac, \( 60 \% \) of adult smokers started smoking before turning 18 years old. (a) Compute the mean and standard deviation of the random variable \( X \), the number of smokers who started before 18 in 300 trials of the probability experiment. (b) Interpret the mean. (c) Would it be unusual to observe 240 smokers who started smoking before turning 18 years old in a random sample of 300 adult smokers? Why? (a) \( \mu_{x}=\square \) You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.001 \). \[ H_{o}: \mu=77.9 \] \( \quad H_{a}: \mu<77.9 \) You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \( n=30 \) with mean \( M=71.7 \) and a standard deviation of \( S D=10.3 \). What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) \( \alpha \) greater than \( \alpha \) This test statistic leads to a decision to... reject the null accept the null fail to reject the null
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