ISU STAT 226 - Exam1practice (5 pages)

Stat 226 Exam 1 Practice Questions 1 TRUE or FALSE Identify which of the following are valid statements and which ones are false a T F All density curves are symmetric b T F Prior to analyzing any data one should always check for outlying observations and if present delete these to avoid biased results c T F Dataset X has n 100 observations Suppose I order all observations from smallest to largest and obtain a value of 44 for the IQR If I increase the LARGEST observation by any positive number in Dataset X then the IQR will change d T F Dataset Y has n 100 observations all equal to 25 Dataset Z has n 50 observations all equal to 50 The variance of Dataset Y is equal to the variance of Dataset Z e T F The sampling distribution of the sample mean allows us to compute how likely it is to observe a sample mean falling within a particular range of values f T F The random variable Z can be described by a Standard Normal distribution The range of Z is between 3 49 and 3 49 i e Z can take on any value between 3 49 and 3 49 g T F In a histogram a larger bin width is associated with a bigger loss of information h T F When the sample size n increases the variance of the corresponding sampling distribution increases i T F Zip codes are an example of an ordinal categorical variable 2 Obesity Epidemic Revisited In 2010 body mass index BMI for male adults followed a Normal distribution with mean 27 8 and standard deviation 5 5 A man is considered obese if he has a BMI greater than 30 a The probability of a male adult from 2010 having a BMI greater than 30 i e classified as obese is 0 3446 Suppose I take a random sample of n men where n 1 What can you say about the probability that the mean BMI of the random sample is greater than 30 Circle One i The probability that the mean BMI for these n men is greater than 30 will be less than 0 3446 ii The probability that the mean BMI for these n men is greater than 30 will be more than 0 3446 iii The probability that the mean BMI for these n men is greater than 30 will be equal to 0 3446 iv There is not sufficient information to answer this question 1 b Suppose I take a simple random sample of 100 men from 2010 i Describe the sampling distribution of the mean BMI for samples of size 100 by answering the following questions a What is the shape of the sampling distribution Circle One Normal Approximately Normal Not Normal b What is the mean of the sampling distribution Do not round answer Final Answer c What is the standard deviation standard error of the sampling distribution Do not round answer Final Answer ii The mean BMI for this sample of 100 men was 28 691 What is the probability of observing this mean BMI or higher for random samples of 100 men Show all your work to receive credit a Report the z score corresponding to 28 691 to 2 decimal places Show work here Final Answer b Report the final probability as a proportion not a percent to 4 decimal places using Table A Show work here Final Answer iii What is the value of the sample mean such that only 6 3 of sample means based on samples of size 100 fall below this value Compute this value and report the answer to 4 decimal places Show all of your work to receive credit Show work here Final Answer 2 3 A set of test scores follows a Normal distribution ie X N 60 10 a Which of the following statements is true Circle one i ii iii iv The standard deviation of X is 602 P 55 X 65 0 6800 P X 60 1 P X 60 0 5 b What is the median of X c What z score corresponds to the 85th percentile of X d Draw the probability density function for X Mark approximately the 85th percentile of X and shade the area to the right of it What X value corresponds to the 85th percentile of X e How much of the total area under the curve is shaded f What is the probability of observing a data point from this distribution inside the shaded area g According to the Empirical Rule 68 of the data falls between what two X values 3 4 Presidential Election As we get closer to the upcoming presidential election on November 8th 2016 many polling companies are eager to produce their predictions as to what percentage of the population will vote for either of the two major candidates Each company has different tactics to contact potential voters across the nation in order to learn about how the country will vote Suppose that a particular company decided to contact a random sample of 2 200 home owners across the country in order to produce their predictions for the presidential election They found that 61 were planning to vote for candidate 1 while 35 planned to vote for candidate 2 a Identify the population of interest Be as specific as you can be If you are uncertain about the required level of detail describe the population such that someone who has not read the above paragraph understands what the population of interest is b Specify one of the two parameters Note that either parameter is fine and will get equal credit Again be as specific as you can and describe the parameters such that someone who has not read the above paragraph understands what the parameters of interest represent c Identify the sample d Specify one of the two statistics Note that either statistic is fine and will get equal credit Again be as specific as you can and describe the statistics such that someone who has not read the above paragraph understands what the statistics are e Is the sample representative of the population Why or why not f In your own words describe the purpose of collecting data and calculating summary statistics g Collecting the data and calculating summary statistics is considered which of the following Circle the appropriate one inferential statistics descriptive statistics neither 4 5 General Multiple Choice Choose the best response a Which of these variables is a categorical variable i ii iii iv v The annual amount of energy consumed in your bedroom Marital status Calories in kcal consumed each day Age in years None of the above b Which of these values is NOT included in a five number summary i ii iii iv v Maximum Q1 First quartile Median Mean 75 percentile c A random sample of 100 salaries from the Des Moines insurance sector are recorded and found to have a median of 110 000 and a mean of 150 000 Based on this information a histogram of these 100 salaries is most likely i ii iii …