Southeast Missouri State University



Review Problems for Final ExamMA155 Fall 2014 ( Sections 2.1 and 2.2)1) The data below represent the results of a poll in which the following question was asked:, “To what degree are you satisfied with the outcome of the 1994 mayoral election?” Which pie chart below represents the given data set?Very 36Somewhat 48Not at All 62No opinion 54 2) State whether the data described are qualitative or quantitative and give their level of measurement.An officer’s rank in the military.Gender of a sample of newborn babies.The year of manufacture of a car.The ranking of students based on MA155 scores.Time taken by the athletes in 100 m race.3) The preschool children at Elmwood Elementary School were asked to name their favorite color. The results are listed below. Construct a frequency distribution and a relative frequency distribution. Display the count in a Pareto chart.yellow yellow blue purple redred red yellow red bluered blue purple purple purpleblue red purple red green4) Retailers are always interested in determining why a customer selected their store to make a purchase. A sporting goods retailer conducted a customer survey to determine why its customers shopped at the store. The results are shown below. What percentage of the customers responded that the merchandise was the reason they shopped at the store? Round to the nearest whole percent.A) 43% B) 30% C) 50% D) 29% 5) For the data below, construct a frequency histogram and a relative frequency histogram.6) Find the original data from the stem–and–leaf plot.7) A nurse measured the blood pressure of each person who visited her clinic. Following is a relative frequency histogram for the systolic blood pressure readings for those people aged between 25 and 40. Use the histogram to answer the question. The blood pressure readings were rounded up to the next whole number. Approximately what percentage of the people aged 25–40 had a systolic blood pressure reading less than or equal to 120?35% B) 3.5% C) 5% D) 50%8) The following graph shows the number of car accidents occurring in one city in each of the years 2006 through 2011 (Year 1 = 2006, Year 2 = 2007 etc). The number of accidents dropped in 2008 after a new speed limit was imposed. How is the bar graph misleading? How would you redesign the graph to be less misleading?9) The following table shows world population data by continent (2000). ContinentPopulation(billions)Asia3.68Africa0.78Europe0.73North America0.31Australia0.03South/Central America0.52Draw a bar graph to display this data.Would a pie chart appropriate for this display? Why?Would a line chart be appropriate for this display? Why or why not? ( sections 3.1, 3.2, 3.4,3.5, 4.1, 4.2, and 4.3)10) The stock market did well during the 1990s. Here are the percent total returns (change in price plus dividends paid) for the Standard & Poor's 500 stock index: Year: 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 Return: 31.7 -3:1 30.5 7.6 10.1 1.3 37.6 23.0 33.4 28.6 The next three questions are related to this situation.The median return during this period is5.5 (b) 20.07 (c) 23.0 (d) 25.8 (e) 28.6The third quartile of these returns is7.6 (b) 30.5 (c) 31.1 (d) 31.7 (e) 33.4The mean return is20.07 (b) 20.69 (c) 22.3 (d) 25.8 (e) 33.411) Here are the survival times (in days) of 46 guinea pigs that were injected with a bacterial infection in a medical study. 43 45 53 56 56 57 58 66 67 73 74 79 80 80 81 81 81 82 83 83 84 88 91 92 92 97 99 99 100 101 102 103 107 109 114 121 126 137 139 145 156 174 179 191 211 243Find the five number summary.Draw Boxplot.What can you say about shape of data distribution?It is clear from inspecting the survival time data (don't calculate the mean) that the mean survival time must be (a) quite a bit larger than the median because the data are right-skewed. (b) quite a bit smaller than the median because the data are right-skewed. (c) quite close to the median. (d) quite a bit larger than the median because the data are left-skewed. (e) quite a bit smaller than the median because the data are left-skewed.v) Find outlier(s) , if any. Show using IQR method. 12) Below is data for two variables X: 1 2 3 4 10 10 Y: 1 3 3 5 1 11Construct a scatterplot of the data and briefly describe the overall pattern.Guess the correlation coefficient.Interpret correlation.Despite linear association between x and y, why is correlation small? 13) Researchers studying acid rain measured the acidity of precipitation in a Colorado wilderness area for 150 consecutive weeks. Acidity is measured by pH. They reported that the following least-squares regression line fits the data well: pH = 5.43 – (0.0053)weeksWhat is the response variable? What is the explanatory variable? Is the relationship between pH and weeks positive or negative. Why? What was the pH at the beginning of the study ( weeks= 1)? At the end ( weeks = 150)?What is the slope of the regression line? Explain what this says about the change in pH of precipitation?Interpret R2 =0.95. Find correlation coefficient ‘r’. 14) The correlation between IQ score and school GPA is r = .634. The correlation between wine consumption and heart disease deaths is r = -0.843. Which of these two correlations indicates a stronger linear relationship? Explain.15) Suppose that the correlation between the scores of students on Exam 1 and Exam 2 in MA155 is r = 0.7. One way to interpret r is to say what percent of the variation in Exam 2 scores can be explained by the straight line relationship between Exam2 scores and Exam 1 scores. The percent is about a) 84% b) 70% c) 49% d) 30% ( Sections 6.1, 7.1, and 7.2)16) Let X be the number of people in a household for a certain community. Consider the following distribution for X: X: 1 2 3 4 5 6 7 p(X): .2 .32 .18 .15 .07 .03 .05a. What is the probability that a randomly chosen household contains more than three people?b. What is the probability that a randomly chosen household contains no more than two people?c. What is the mean number of people in a household?d. What is the probability that a randomly chosen household contains more than two but at most fourpeople.17) The distribution of heights of young men is approximately normal with mean 70 inches and standard deviation 2.5 inches. Use the 68-95-99.7 rule to answer following questions.a) What percent of men are taller than 75 inches?b) Between what heights do the middle 95% of men fall?c) What percent of men are shorter than 67.5 inches?18) The heights of young women are approximately normal with mean 65 inches and standard deviation 2.5 inches. How tall are the tallest 10% of women?19) Scores on the GRE( Graduate Record Exam) are approximately normally distributed with mean 497 and standard deviation 115.a) If a graduate school requires a GRE score of 650 for admission, what proportion of applicants will be eligible for admission?b) If a graduate school will give admission to top 5%, what is the cut off GRE score?20) Determine whether each statement is true or false or fill in the blanks.a) Area to the right of mean of a normal distribution is ___________. b) The special property of the standard normal distribution is that its mean is __ and standard deviation is ____. c) The number of standard deviations that a particular X value is away from the mean is standard score or Z score. d) Using the normal distribution curve, the area under the curve between and is _____.21) All students in a class were asked how many times they had read the city newspaper in the past week The data is in the chart below. No. Times ReadNewspaperProbability00.2510.0520.1030.1040.1550.35What is the probability that someone randomly selected will read the newspaper more than 3 times in the past week?What is the probability that someone randomly selected will read the newspaper at most two times in the past week?What is the probability that someone randomly selected will read the newspaper between 1 and 4 times in the past week?What is the mean number of times that someone will have read the newspaper in the past 5 days?22) Your professor returns a set of exams to the class and announces that the Distribution of scores followed an approximate normal distribution with mean of 78 points and a standard deviation of 5 points. He also announces that top 10% of the test scores will get an ‘A’. You received 87 points. Did you get ‘A’? Why? Why not?23) At a large government office center in Jackson, it has been found that the time employees spend on the phone each day for business purposes has a normal distribution with mean 47 minutes and standard deviation 10 minutes. What is the probability that randomly selected employee spends from 27 to 47 minutes on the phone each day?What is the probability that randomly selected employee spends more than 57 minutes on the phone each day?What is the probability that randomly selected employee will spend less than 50 minutes on phone each day?What is the 90th percentile?( sections 8.1, 9.1, 9.2, 10.1, and 10.2)Nine employees of a company are selected at random and asked how far they commute to work each day. The distances (in miles) are as follows: 32, 18, 44, 29, 25, 38, 5, 48, 12. Estimate the mean commute distance of all employees of the company.It is not possible to estimate the population mean from this sample data. 26.7 miles 27.9 miles 29 milesThe ages of employees at a particular company have a mean of 39 and standard deviation 0f 11. Suppose you take a sample of 200 employees from the company and find that their mean age is 41.3. How many standard deviations is the sample mean above the mean of the sampling distribution?2.342.95 41.20.21The inside diameter of a randomly selected piston ring is a random variable with mean value 12 cm and standard deviation .04 cm.If is the sample mean diameter from a random sample of n=16 rings, where is the sampling distribution of centered, and what is the standard error of ?Answer the questions above for a sample of size n = 64.Find the probability that the average diameter of piston rings from a sample of size 16 is more than 11.5 cm.For which of the above two random samples, is more likely to be within .01 cm of 12 cm? Explain.In one city, there are a total of 1640 5-year-old children of whom 553 live with one parent only. Among a sample of 600 of the 5-year-old children from this city, 223 live with one parent only. Find the sample proportion of 5-year-old children who live with only one parent..34.37.40223In one city, there are a total of 1780 5-year old children of whom 556 live with one parent only. Among a sample of 615 of the 5-year old children from this city, 226 live with one parent only. Find the population proportion of 5-year olds who live with only one parent.A) 0.35 B) 556 C) 0.37 D) 0.31 At one hospital, a random sample of 100 women giving birth to their first child is selected. Among this sample, the mean age was 25.7 with a standard deviation of 5.1. Estimate the mean age of all women giving birth to their first child at this hospital. Give the 95% confidence interval two decimal places.A medical researcher wishes to estimate the mean systolic blood pressure of heart surgery patients the day following surgery. She desires a margin of error of 1.6 mm Hg. Past studies suggest that a population standard deviation of 43 mm Hg is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.A researcher collects the weight (in pounds) of a random sample of 32 new born babies, born at a particular hospital. Give the 99% confidence interval to two decimal places. The sample mean is 7.19 pounds and the standard deviation is 0.844 pounds.A researcher wishes to estimate the proportion of left-handers among a certain population. In a random sample of 900 people from the population, 74% are left-handed. Find the margin of error for the 95% confidence interval.A researcher wishes to estimate the proportion of left-handers among a certain population. In a random sample of 990 people from the population, 36.4% are left-handed. Find the 95% confidence interval for the population proportion of left-handers to four decimal places.A population proportion is to be estimated. Estimate the minimum sample size needed to achieve a margin of error of E = 0.056 with a 95% degree of confidence. A medical researcher wishes to estimate proportion of babies born at a particular hospital by Caesarean section. In a random sample of 100 births at the hospital, 34% were Caesarean sections. Find the 95% confidence interval for the population proportion.A population proportion is to be estimated. Estimate the minimum sample size needed to achieve a margin of error of 7 percentage points with a 95% degree of confidence. A Past study estimated the proportion to be 0.63.Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed and what parameter is being tested?According to the Centers for Disease Control and Prevention, 19.6% of children aged 6-11 years are overweight. A school nurse thinks that the percentage of 6-11 year olds who are overweight is higher in her school.Determine null and alternative hypotheses.Explain what it means to make Type I error.Explain what it means to make Type II error.The mean score on the SAT Math Reasoning exam is 516. A test preparation company states that the mean score of students who take its course is higher than 516.Determine null and alternative hypotheses.If sample data indicate that the null hypothesis should not be rejected, state the conclusion of the company.Suppose, in fact, that the mean score of students taking the preparatory course is 522. Has a Type I or Type II error been made?If we tested the hypothesis at α = 0.01, what is the probability of committing Type I error.It has been claimed that at U.C.L.A. 40% of the students live on campus. From a sample of 250 students, 90 live on campus. Determine null and alternative hypotheses.What is the point estimate for population proportion?Does the evidence support this claim at ? Use classical method and state the conclusion.StatCrunch ResultProportionCountTotalSample Prop.Std. Err.Z-StatP-valuep902500.360.031-1.290.197According to the U.S. Census Bureau, in 2009, 7.8% of Americans had a travel time to work of more than 60 minutes. An urban economist believes that this percentage has increased since 2009. She randomly selects 80 working Americans and finds that 11 of them have a travel time to work that is more than 60 minutes.Determine null and alternative hypotheses.What is the point estimate for population proportion?Does the evidence support this claim at α = 0.05? Use P-value method and state the conclusion.StatCrunch ResultProportionCountTotalSample Prop.Std. Err.Z-StatP-valuep11800.1380.02991.980.0236The college daily reported: “600 students living in university housing were polled. 360 said that they were satisfied with their living conditions. Based on this survey we conclude that 60% of students living in dormitories are satisfied. The margin of error of the study is 4 percentage points (with a 95% degree of confidence).” Which statement is correct?There is not enough information to determine whether the margin of error is consistent with the sample size. The stated margin of error could have been achieved with a smaller sample size. A larger ample size should be used to achieve the stated margin of error. The margin of error is consistent with sample size. ................
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