# Penn State STAT 200 Quiz Set 5 with 100% Correct Solution Guaranteed

1.Correcly identify if the following random variables as either discrete or continous. The time taken to run a marathonA) ContinuousB) Discrete2.Correctly identify whether the following situations satisfy the conditions required to conduct a Binomial experiment. Selecting a few voters from a very large population of voters and observing whether or not each of them favors a certain proposition in an election when 54% of all voters are known to be in favor of this proposition.A) NOT BinomialB) Binomial3.From the table above, What is the probability that only two college students in this sample abstain from drinking?A) 0.1536B) 0.4096C) 0.8192D) 0.97284.The expected value for a random variable isA) always np.B) the most likely value.C) the long-run average.D) the most frequent value observed in a random sample of observations of the random variable.5.The probability is p = 0.80 that a patient with a certain disease will be successfully treated with a new medical treatment. Suppose that the treatment is used on 40 patients. What is the expected value of the number of patients who are successfully treated?A) 20B) 8C) 32D) 406.For a normal random variable (Using Standard Normal Table), what is the probability of an observation being greater than the mean but less than one standard deviation above the mean?A) 0.6826B) 0.1587C) 0.5000D) 0.34137.The time taken for a computer to boot up, X, follows a normal distribution with mean 30 seconds and standard deviation 5 seconds. What is the standardized score (z-score) for a boot-up time of x =20 seconds?A) 2.0B) 0.0C) -2.0D) 1.08.Which of the following statements is correct about a parameter and a statistic associated with repeated random samples of the same size from the same population?A) Values of a parameter will vary from sample to sample but values of a statistic will not.B) Values of a statistic will vary according to the sampling distribution for that statistic.C) Values of a parameter will vary according to the sampling distribution for that parameter.D) Values of both a parameter and a statistic may vary from sample to sample.9.For which of the following situations would the Rule for Sample Proportions (i.e. we could say that the sample proportion distribution approximates a normal distribution) not apply?A) A random sample of 50 is taken from a population in which the proportion with the trait of interest is 0.50.B) A random sample of 100 is taken from a population in which the proportion with the trait of interest is 0.98.C) A binomial experiment is done with n = 500 and p = 0.9.10.Suppose on a highway with a speed limit of 65 mph, the speed of cars are independent and normally distributed with an average speed = 65 mph and standard deviation = 5 mph. What is the expected value of the sample mean speed in a random sample of n = 10 cars?A) 6.5 mphB) 20.55 mphC) 65 mphD) 13 mph11.Is the given percent a statistic or a parameter? 75% of all students at a school are in favor of more bicycle parking spaces on campus.A) ParameterB) Statistic12.Which statement is true about x-bar and ?-hat?A) x-bar is a parameter and ?-hat is a statistic.B) They are both statistics.C) They are both parameters.D) ?-hat is a parameter and x-bar is a statistic.13.Based on the 2000 Census, 31.8% of grandparents in California are the primary caregivers for their grandchildren. Suppose n = 1000 persons are to be sampled from this population and the sample proportion of grandparents as primary caregivers (?-hat) is to be calculated. What is the mean of the sampling distribution of ?-hat?A) 0.2169B) 0.3180C) 0.0147D) 0.000214.Based on the 2000 Census, 31.8% of grandparents in California are the primary caregivers for their grandchildren. Suppose n = 1000 persons are to be sampled from this population and the sample proportion of grandparents as primary caregivers (?-hat) is to be calculated. What is the standard deviation of the sampling distribution of ?-hat?A) 0.2169B) 0.3180C) 0.0002D) 0.014715.Suppose on a highway with a speed limit of 65 mph, the speed of cars are independent and normally distributed with an average speed = 65 mph and standard deviation = 5 mph. What is the standard deviation for the sample mean speed in a random sample of n = 100 cars?A) 0.5B) 13C) 3.2516.The z* multiplier for a 90% confidence interval isA) 1.65B) 2.58C) 2.33D) 1.9617.A random sample of 600 adults is taken from a population of over one million, in order to compute a confidence interval for a proportion. If the researchers wanted to decrease the width of the confidence interval, they couldA) decrease the size of the population.B) increase the size of the population.C) increase the size of the sample.D) decrease the size of the sample.18.Which statement is not true about confidence intervals?A) A confidence interval between 20% and 40% means that the population proportion lies between 20% and 40%.B) A 99% confidence interval procedure has a higher probability of producing intervals that will include the population parameter than a 95% confidence interval procedure.C) An approximate formula for a 95% confidence interval is sample estimate Â± margin of error.D) A confidence interval is an interval of values computed from sample data that is likely to include the true population value.19.In a survey of n = 950 randomly selected individuals, 17% answered yes to the question “Do you think the use of marijuana should be made legal or not?” A 90% confidence interval for the proportion of all Americans in favor of legalizing marijuana isA) 0.139 to 0.201B) 0.150 to 0.190C) 0.142 to 0.198D) 0.146 to 0.19420.Suppose that a confidence interval for a population proportion p is to be calculated. For a sample size n = 1000 and sample proportion p-hat = 0.35 what is the approximate margin of error for a 95% confidence interval?A) 0.025B) 0.011C) 0.0003D) 0.03021.In a past General Social Survey, a random sample of men and women answered the question “Are you a member of any sports groups?” Based on the sample data, 95% confidence intervals for the population proportion who would answer yes are 0.13 to 0.19 for women and 0.25 to 0.33 for men. Based on these results, you can reasonably conclude thatA) there is no conclusive evidence of a gender difference in the proportions of men and women who belong to sports clubs.B) at least 25% of American men and American women belong to sports clubs.C) there is conclusive evidence of a gender difference in proportions of American men and American women who belong to sports clubs.22.Which of the following statements is most correct about a confidence interval for a mean?A) It provides a good guess for the range of values the population mean is likely to have in repeated samples.B) It provides a range of values, any of which is a good guess at the possible value of the population mean.C) It provides a good guess for the range of values the sample mean is likely to have in repeated samples.D) It provides a range of values, any of which is a good guess at the possible value of the sample mean.23.A randomly selected sample of n =51 men in Brazil had an average lifespan of 59 years. The standard deviation was 10 years and the standard error was 1.400. Calculate a 98% confidence interval for the average lifespan for all men in Brazil.A) (35.0, 83.0)B) (55.6, 62.4)C) (56.2, 61.8)24.Suppose that 200 different polling organizations and academic researchers all do surveys in which the same question is asked. All 200 research groups construct a 90% confidence interval for the proportion who would say “yes” to this question. About how many of the 200 different 90% confidence intervals will capture the value of the population proportion?A) 95B) 90C) 180D) 190
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# Penn State STAT 200 Quiz Set 5 with 100% Correct Solution Guaranteed

1.Correcly identify if the following random variables as either discrete or continous. The time taken to run a marathonA) ContinuousB) Discrete2.Correctly identify whether the following situations satisfy the conditions required to conduct a Binomial experiment. Selecting a few voters from a very large population of voters and observing whether or not each of them favors a certain proposition in an election when 54% of all voters are known to be in favor of this proposition.A) NOT BinomialB) Binomial3.From the table above, What is the probability that only two college students in this sample abstain from drinking?A) 0.1536B) 0.4096C) 0.8192D) 0.97284.The expected value for a random variable isA) always np.B) the most likely value.C) the long-run average.D) the most frequent value observed in a random sample of observations of the random variable.5.The probability is p = 0.80 that a patient with a certain disease will be successfully treated with a new medical treatment. Suppose that the treatment is used on 40 patients. What is the expected value of the number of patients who are successfully treated?A) 20B) 8C) 32D) 406.For a normal random variable (Using Standard Normal Table), what is the probability of an observation being greater than the mean but less than one standard deviation above the mean?A) 0.6826B) 0.1587C) 0.5000D) 0.34137.The time taken for a computer to boot up, X, follows a normal distribution with mean 30 seconds and standard deviation 5 seconds. What is the standardized score (z-score) for a boot-up time of x =20 seconds?A) 2.0B) 0.0C) -2.0D) 1.08.Which of the following statements is correct about a parameter and a statistic associated with repeated random samples of the same size from the same population?A) Values of a parameter will vary from sample to sample but values of a statistic will not.B) Values of a statistic will vary according to the sampling distribution for that statistic.C) Values of a parameter will vary according to the sampling distribution for that parameter.D) Values of both a parameter and a statistic may vary from sample to sample.9.For which of the following situations would the Rule for Sample Proportions (i.e. we could say that the sample proportion distribution approximates a normal distribution) not apply?A) A random sample of 50 is taken from a population in which the proportion with the trait of interest is 0.50.B) A random sample of 100 is taken from a population in which the proportion with the trait of interest is 0.98.C) A binomial experiment is done with n = 500 and p = 0.9.10.Suppose on a highway with a speed limit of 65 mph, the speed of cars are independent and normally distributed with an average speed = 65 mph and standard deviation = 5 mph. What is the expected value of the sample mean speed in a random sample of n = 10 cars?A) 6.5 mphB) 20.55 mphC) 65 mphD) 13 mph11.Is the given percent a statistic or a parameter? 75% of all students at a school are in favor of more bicycle parking spaces on campus.A) ParameterB) Statistic12.Which statement is true about x-bar and ?-hat?A) x-bar is a parameter and ?-hat is a statistic.B) They are both statistics.C) They are both parameters.D) ?-hat is a parameter and x-bar is a statistic.13.Based on the 2000 Census, 31.8% of grandparents in California are the primary caregivers for their grandchildren. Suppose n = 1000 persons are to be sampled from this population and the sample proportion of grandparents as primary caregivers (?-hat) is to be calculated. What is the mean of the sampling distribution of ?-hat?A) 0.2169B) 0.3180C) 0.0147D) 0.000214.Based on the 2000 Census, 31.8% of grandparents in California are the primary caregivers for their grandchildren. Suppose n = 1000 persons are to be sampled from this population and the sample proportion of grandparents as primary caregivers (?-hat) is to be calculated. What is the standard deviation of the sampling distribution of ?-hat?A) 0.2169B) 0.3180C) 0.0002D) 0.014715.Suppose on a highway with a speed limit of 65 mph, the speed of cars are independent and normally distributed with an average speed = 65 mph and standard deviation = 5 mph. What is the standard deviation for the sample mean speed in a random sample of n = 100 cars?A) 0.5B) 13C) 3.2516.The z* multiplier for a 90% confidence interval isA) 1.65B) 2.58C) 2.33D) 1.9617.A random sample of 600 adults is taken from a population of over one million, in order to compute a confidence interval for a proportion. If the researchers wanted to decrease the width of the confidence interval, they couldA) decrease the size of the population.B) increase the size of the population.C) increase the size of the sample.D) decrease the size of the sample.18.Which statement is not true about confidence intervals?A) A confidence interval between 20% and 40% means that the population proportion lies between 20% and 40%.B) A 99% confidence interval procedure has a higher probability of producing intervals that will include the population parameter than a 95% confidence interval procedure.C) An approximate formula for a 95% confidence interval is sample estimate Â± margin of error.D) A confidence interval is an interval of values computed from sample data that is likely to include the true population value.19.In a survey of n = 950 randomly selected individuals, 17% answered yes to the question “Do you think the use of marijuana should be made legal or not?” A 90% confidence interval for the proportion of all Americans in favor of legalizing marijuana isA) 0.139 to 0.201B) 0.150 to 0.190C) 0.142 to 0.198D) 0.146 to 0.19420.Suppose that a confidence interval for a population proportion p is to be calculated. For a sample size n = 1000 and sample proportion p-hat = 0.35 what is the approximate margin of error for a 95% confidence interval?A) 0.025B) 0.011C) 0.0003D) 0.03021.In a past General Social Survey, a random sample of men and women answered the question “Are you a member of any sports groups?” Based on the sample data, 95% confidence intervals for the population proportion who would answer yes are 0.13 to 0.19 for women and 0.25 to 0.33 for men. Based on these results, you can reasonably conclude thatA) there is no conclusive evidence of a gender difference in the proportions of men and women who belong to sports clubs.B) at least 25% of American men and American women belong to sports clubs.C) there is conclusive evidence of a gender difference in proportions of American men and American women who belong to sports clubs.22.Which of the following statements is most correct about a confidence interval for a mean?A) It provides a good guess for the range of values the population mean is likely to have in repeated samples.B) It provides a range of values, any of which is a good guess at the possible value of the population mean.C) It provides a good guess for the range of values the sample mean is likely to have in repeated samples.D) It provides a range of values, any of which is a good guess at the possible value of the sample mean.23.A randomly selected sample of n =51 men in Brazil had an average lifespan of 59 years. The standard deviation was 10 years and the standard error was 1.400. Calculate a 98% confidence interval for the average lifespan for all men in Brazil.A) (35.0, 83.0)B) (55.6, 62.4)C) (56.2, 61.8)24.Suppose that 200 different polling organizations and academic researchers all do surveys in which the same question is asked. All 200 research groups construct a 90% confidence interval for the proportion who would say “yes” to this question. About how many of the 200 different 90% confidence intervals will capture the value of the population proportion?A) 95B) 90C) 180D) 190
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