Month: September 2017

Find z for each of the following confidence levels. Round to two decimal places. 90% 95% 96% 97% 98% 99% 2. For a data set obtained from a random sample, n = 81 and x = 48.25. It is known that ? = 4.8. What is the point estimate of ?? Round to two decimal places Make a 95% confidence interval for ?. What is the lower limit? Round to two decimal places. Make a 95% confidence interval for ?. What is the upper limit? Round to two decimal places. What is the margin of error of estimate for part b? Round to two decimal places. 3. Determine the sample size (nfor the estimate of ? for the following. E = 2.3, ? = 15.40, confidence level = 99%. Round to the nearest whole number. E = 4.1, ? = 23.45, confidence level = 95%. Round to the nearest whole number. E = 25.9, ? = 122.25, confidence level = 90%. Round to the nearest whole number. 4. True or False. a.The null hypothesis is a claim about a population parameter that is assumed to be false until it is declared false. True False b. An alternative hypothesis is a claim about a population parameter that will be true if the null hypothesis is false. True False c. The critical point(s) divide(s) is some of the area under a distribution curve into rejection and nonrejection regions. True False d. The significance level, denoted by ?, is the probability of making a Type II error, that is, the probability of rejecting the null hypothesis when it is actually true. True False e. The nonrejection region is the area to the right or left of the critical point where the null hypothesis is not rejected. True False 5. Fill in the blank. The level of significance in a test of hypothesis is the probability of making a ________. It is the area under the probability distribution curve where we reject H0. Type I error Type II error Type III error 6. Consider H0: ? = 45 versus H1: ? < 45. A random sample of 25 observations produced a sample mean of 41.8. Using ? = .025 and the population is known to be normally distributed with ? = 6. What is the value of z? Round to two decimal places. Would you reject the null hypothesis? Reject Ho Do not reject Ho 7. The following information is obtained from two independent samples selected from two normally distributed populations. n1 = 18 x1 = 7.82 ?1 = 2.35 n2 =15 x2 =5.99 ?2 =3.17 A. What is the point estimate of ?1 ? ?2? Round to two decimal places. B. Construct a 99% confidence interval for ?1 ? ?2. Find the margin of error for this estimate. Round to two decimal places. 8. The following information is obtained from two independent samples selected from two populations. n1 =650 x1 =1.05 ?1 =5.22 n2 =675 x2 =1.54 ?2 =6.80 Test at a 5% significance level if ?1 is less than ?2. Identify the appropriate distribution to use. t distribution normal distribution What is the conclusion about the hypothesis? Reject Ho Do not reject Ho 9. Using data from the U.S. Census Bureau and other sources, www.nerdwallet.com estimated that considering only the households with credit card debts, the average credit card debt for U.S. house- holds was $15,523 in 2014 and $15,242 in 2013. Suppose that these estimates were based on random samples of 600 households with credit card debts in 2014 and 700 households with credit card debts in 2013. Suppose that the sample standard deviations for these two samples were $3870 and $3764, respectively. Assume that the standard deviations for the two populations are unknown but equal. Let ?1 and ?2 be the average credit card debts for all such households for the years 2014 and 2013, respectively. What is the point estimate of ?1 ? ?2? Round to two decimal places. Do not include the dollar sign. Construct a 98% confidence interval for ?1 ? ?2. Round to two decimal places. Do not include the dollar sign. What is the lower bound? Round to two decimal places. What is the upper bound? Round to two decimal places. Using a 1% significance level, can you conclude that the average credit card debt for such households was higher in 2014 than in 2013? Use both the p-value and the critical-value approaches to make this test. Reject Ho Do not reject Ho 10. Gamma Corporation is considering the installation of governors on cars driven by its sales staff. These devices would limit the car speeds to a preset level, which is expected to improve fuel economy. The company is planning to test several cars for fuel consumption without governors for 1 week. Then governors would be installed in the same cars, and fuel consumption will be monitored for another week. Gamma Corporation wants to estimate the mean difference in fuel consumption with a margin of error of estimate of 2 mpg with a 90% confidence level. Assume that the differences in fuel consumption are normally distributed and that previous studies suggest that an estimate of sd=3sd=3 mpg is reasonable. How many cars should be tested? (Note that the critical value of tt will depend on nn, so it will be necessary to use trial and error.)

.Let x be a continuous random variable. What is the probability that x assumes a single value, such as a (use numerical value)? 2. The following are the three main characteristics of a normal distribution. The total area under a normal curve equals _____. A normal curve is ___________ about the mean. Consequently, 50% of the total area under a normal distribution curve lies on the left side of the mean, and 50% lies on the right side of the mean. Fill in the blank. The tails of a normal distribution curve extend indefinitely in both directionswithout touching or crossing the horizontal axis. Although a normal curve never meets the ________ axis, beyond thepoints represented by µ -3? to µ+3?it becomes so close to thisaxis that the area under the curve beyond these points in both directions is very close to zero. 3. For the standard normal distribution, find the area within one standard deviation of the mean that is, the area between ? ? ? and ? + ?.Round to four decimal places. 4.Find the area under the standard normal curve. Round to four decimal places. a)between z = 0 and z = 1.95 b)between z = 0 and z = ?2.05 c)between z = 1.15 and z = 2.37 d)from z = ?1.53 to z = ?2.88 e)from z = ?1.67 to z = 2.24 5.ThedatatheTable7.2providesanitTheacalledTable7.5providesan A.Probability distribution B.Population distribution C.Normal distribution D.Sampling distribution 6. ___________ is the difference between the value of the sample statistic and the value ofthe corresponding population parameter, assuming that the sample is random and nonon-sampling error has been made. Example 7–1 in the text displays sampling error. Sampling error occurs only in sample surveys. 7. Consider the following population of 10 numbers. 20 25 13 19 9 15 11 7 17 30 a)Find the population mean. Round to two decimal places. b)Rich selected one sample of nine numbers from this population. The sample included the numbers 20, 25, 13, 9, 15, 11, 7, 17, and 30. Calculate sampling error for this sample. Round to decimal places. 8. Fill in the blank. The F distribution is ________ and skewed to the right. The Fdistribution hastwo numbers of degrees of freedom: dffor the numerator and dffor the denominator. The unitsof an Fdistribution, denoted by F, are nonnegative. 9. Find the critical value of F for the following. Round to two decimal places. a)df = (3, 3) and area in the right tail = .05 b)df = (3, 10) and area in the right tail = .05 c)df = (3, 30) and area in the right tail = .05 10. The following ANOVA table, based on information obtained for three samples selected from three independent populations that are normally distributed with equal variances, has a few missing values. Source of Variation Degrees of Freedom Sum of Squares Mean Square Value of the Test Statistic Between 2 II 19.2813 Within 89.3677 III F = ___V__ = VII VI Total 12 IV a)Find the missing values and complete the ANOVA table. Round to four decimal places. b)Using ? = .01, what is your conclusion for the test with the null hypothesis that the means of the three populations are all equal against the alternative hypothesis that the means of the three populations are not all equal? Reject H0. Conclude that the means of the three populations are equal. Reject H0. Conclude that the means of the three populations are not equal. Do not reject H0. Conclude that the means of the three populations are equal. Do not reject H0. Conclude that the means are of the three populations are not equal.

. List the simple events for each of the following statistical experiments in a sample space. a)One roll of a die. Note: Separate your response with a comma (,). For example 22, 23, 24 b)Three tosses of a coin. Note: Use this notation for your answer. heads = H. tails = T. For example HT, TH c)One toss of a coin and one roll of a die. Note: Use this notation. Heads = H or numbers 1, 2, 3, 4, 5, 6 for the dice. For example H1 indicates heads and dice roll equal to 1. 2. Two students are randomly selected from a statistics class, and it is observed whether or not they suffer from math anxiety. Indicate which are simple and which are compound events. a)Both students suffer from math anxiety. b)Exactly one student suffers from math anxiety. c)The first student does not suffer and the second suffers from math anxiety. d)None of the students suffers from math anxiety. 3. A hat contains 40 marbles. Of them, 18 are red and 22 are green. If one marble is randomly selected out of this hat. a)What is the probability that this marble is red (round to two decimal places)? b)What is the probability that this marble is green (round to two decimal places? 4. Two thousand randomly selected adults were asked whether or not they have ever shopped on the Internet. The following table gives a two-way classification of the responses. Have Shopped Have Never Shopped Male 500 700 Female 300 500 a)If one adult is selected at random from these 2000 adults, find the probability that this adult has never shopped on the Internet. b)If one adult is selected at random from these 2000 adults, find the probability that this adult is a male. c)If one adult is selected at random from these 2000 adults, find the probability that this adult has shopped on the Internet given that this adult is a female. d)If one adult is selected at random from these 2000 adults, find the probability that this adult is a male given that this adult has never shopped on the Internet. 5. Find the joint probability of AA and BB for the following. a) and b) and 6. Classify each of the following random variables as discrete or continuous. a)The time left on a parking meter b)The number of bats broken by a major league baseball team in a season c)The number of cars in a parking lot at a given time d)The price of a car e)The number of cars crossing a bridge on a given day f)The time spent by a physician examining a patient g)The number of books in a student’s bag 7. The following table gives the probability distribution of a discrete random variable x. x 0 1 2 3 4 5 6 P(x) .11 .19 .28 .15 .12 .09 .06 Find the following probabilities. a) b)Probability that assumes a value less than 4. Probability that x assumes a value greater than 2. 8. A limousine has eight tires on it. A fleet of such limos was fit with a batch of tires that mistakenly passed quality testing. The following table lists the probability distribution of the number of defective tires on this fleet of limos where xx represents the number of defective tires on a limo and P(x) is the corresponding probability. x 0 1 2 3 4 5 6 7 8 P(x) .0454 .1723 .2838 .2669 .1569 .0585 .0139 .0015 .0008 Calculate the mean and standard deviation of this probability distribution. Give a brief interpretation of the values of the mean and standard deviation. 9. Let xx be a discrete random variable that possesses a binomial distribution. Using the binomial formula, find the following probabilities. a)(5) for and b)(3) for and Verify your answers by using Table I of Appendix B. 10. Let x be a discrete random variable that possesses a binomial distribution. If n = 5 and p = 0.8, then… a)What is the mean (round to three decimal places) b)What is the standard deviation of the probability distribution (round to three decimal places)?

1. The following table lists the number of deaths by cause as reported by the .cdc.gov/”>Centers for Disease Control and Prevention on February 6, 2015: Cause of Death Number of Deaths Heart disease 611,105 Cancer 584,881 Accidents 130,557 Stroke 128,978 Alzheimer’s disease 84,767 Diabetes 75,578 Influenza and Pneumonia ?56,979 Suicide ?41,149 What is the variable for this data set (use words)? How many observations are in this data set (numeral)? How many elements does this data set contain (numeral)? 2. Indicate which of the following variables are quantitative and which are qualitative. Note:Spell quantitative and qualitative in lower case letters. The amount of time a student spent studying for an exam The amount of rain last year in 30 cities The arrival status of an airline flight (early, on time, late, canceled) at an airport A person’s blood type The amount of gasoline put into a car at a gas station 3. A local gas station collected data from the day’s receipts, recording the gallons of gasoline each customer purchased. The following table lists the frequency distribution of the gallons of gas purchased by all customers on this one day at this gas station. Gallons of Gas Number of Customers 4 to less than 8 ?78 8 to less than 12 ?49 12 to less than 16 ?81 16 to less than 20 117 20 to less than 24 ?13 How many customers were served on this day at this gas station? Find the class midpoints. Do all of the classes have the same width? If so, what is this width? If not, what are the different class widths? What percentage of the customers purchased between 4 and 12 gallons? (do not include % sign. Round numerical value to one decimal place) 4. The following data give the one-way commuting times (in minutes) from home to work for a random sample of 50 workers. 23 17 34 26 18 33 46 42 12 37 44 15 22 19 28 32 18 39 40 48 16 11 ?9 24 18 26 31 ?7 30 15 18 22 29 32 30 21 19 14 26 37 25 36 23 39 42 46 29 17 24 31 What is the frequency for each class 0–9, 10–19, 20–29, 30–39, and 40–49. Calculate the relative frequency and percentage for each class. What percentage of the workers in this sample commute for 30 minutes or more? Note:Round relative frequency to two decimal places. Complete the table by calculating the frequency, relative frequency, and percentage. Commuting Times Frequency (part a) Relative Frequency (part c) Percentage (%) (part d) 0-9 ? 0.?? ? 10-19 ? 0.?? ? 20-29 ? 0.?? ? 30-39 ? 0.?? ? 40-49 ? 0.?? ? 5. The following data give the number of text messages sent on 40 randomly selected days during 2015 by a high school student. 32 33 33 34 35 36 37 37 37 37 38 39 40 41 41 42 42 42 43 44 44 45 45 45 47 47 47 47 47 48 48 49 50 50 51 52 53 54 59 61 Each stem has been displayed (left column). Complete this stem-and-leaf display for these data. Note: Use a space in between each leaf. For example 1 2 3 4 5 6 7 8 9 (do not use this format 123456789). 3 ?… 4 ?… 5 ?… 6 ?… 6 A) Which of the five measures of center (the mean, the median, the trimmed mean, the weighted mean, and the mode) can be calculated for quantitative data only. B) Which can be calculated for both quantitative and qualitative data? 7. Prices of cars have a distribution that is skewed to the right with outliers in the right tail. Which of the measures of center is the best to summarize this data set? 8. The following data give the amounts (in dollars) of electric bills for November 2015 for 12 randomly selected households selected from a small town. 205 265 176 314 243 192 297 357 238 281 342 259 Calculate the (a) mean, (b) median and (c) Is there a mode (Yes or No)? 9. The following data give the prices of seven textbooks randomly selected from a university bookstore. $89 $170 $104 $113 $56 $161 $147 a) Find the mean for these data (input the numerical value without the dollar sign). Calculate the deviations of the data values from the mean. b) Is the sum of these deviations zero (yes or no)? c) Calculate the range (do not include unit). d) Calculate the variance. e) Calculate the standard deviation (round to one decimal place). 10. The following data give the speeds of 13 cars (in mph) measured by radar, traveling on I-84. 73 75 69 68 78 69 74 76 72 79 68 77 71 Find the values of the three quartiles and the interquartile range. Calculate the (approximate) value of the 35th percentile (round to two decimal places). Compute the percentile rank of 71 (round to two decimal places. Do not include the % symbol). Note: Round to two decimal places. Do not include unit.