Stat 226 Exam 1: Practice Questions1. 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 presentdelete these to avoid biased results.(c) T F ”Dataset X” has n = 100 observations. Suppose I order all observations from smallest tolargest and obtain a value of 44 for the IQR. If I increase the LARGEST observation by anypositive 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 observationsall 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 observea 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 ofZ 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 distributionincreases.(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 Normaldistribution with mean, µ = 27.8 and standard deviation, σ = 5.5. A man is considered obese if hehas 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 theprobability 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 than0.3446.ii. The probability that the mean BMI for these “n” men is greater than 30 will be more than0.3446.iii. The probability that the mean BMI for these “n” men is greater than 30 will be equal to0.3446.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 thefollowing 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 notround answer.Final Answer:ii. The mean BMI for this sample of 100 men was 28.691. What is the probability of observingthis mean BMI or higher for random samples of 100 men? Show all your work to receivecredit.(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 usingTable 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 samplesof size 100 fall below this value? Compute this value and report the answer to 4 decimalplaces. Show all of your work to receive credit.Show work here:Final Answer:23. A set of test scores follows a Normal distribution, ie. X ∼ N(60, σ = 10).(a) Which of the following statements is true? Circle one.i. The standard deviation of X is 602.ii. P (55 < X < 65) = 0.6800.iii. P (X < 60) = 1.iv. P (X > 60) = 0.5.(b) What is the median of X?(c) What z-score corresponds to the 85thpercentile of X?(d) Draw the probability density function for X. Mark (approximately) the 85thpercentile of X andshade the area to the right of it. What X value corresponds to the 85thpercentile 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?34. 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 thepopulation will vote for either of the two major candidates. Each company has different tactics tocontact potential voters across the nation in order to learn about how the country will vote. Supposethat a particular company decided to contact a random sample of 2,200 home owners across the countryin order to produce their predictions for the presidential election. They found that 61% were planningto 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 therequired level of detail describe the population such that someone who has not read the aboveparagraph 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 readthe 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 aboveparagraph 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 neither45. General Multiple Choice. Choose the best response.(a) Which of these variables is a categorical variable?i. The annual amount of energy consumed in your bedroomii. Marital statusiii. Calories (in kcal) consumed each dayiv. Age (in years)v. None of the above(b) Which of these values is NOT included in a five number summary:i. Maximumii. Q1(First quartile)iii. Medianiv. Meanv. 75% percentile(c) A random sample of 100 salaries from the Des Moines insurance sector are recorded and foundto have a median of $110,000 and a mean of $150,000. Based on this