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Syed AzmathOsmania University - OU

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Chapter 3 Statistics for Describing, Exploring and Comparing Data Name: 1. The given data represent the number of people from a town, aged 25-64, who subscribe to a print magazine. Age People (Frequency of Midooint y 10 25-34 163 35-44 694 45 - 54 533 55-64 162 Total N/A (a) Construct a frequency polygon using the data. (b) Applying a loose interpretation of the requirements for a normal distribution, does the data appear to be normal distributed? Why or why not? (c) Find the mean of the data summarized in the given frequency distribution. 2. Listed below are the annual tuition amounts of the 10 most expensive colleges in a country for a recent year. $52,797 $53,816 $53,989 $53,906 $53,864 $53,171 $52,087 $52,661 $51,622 $53,989 (a) Find the mean (Round to one decimal places as needed.) (b) Find the midrange. (Round to one decimal places as needed.) (c) Find the median (Round to one decimal places as needed.) (d) What is (are) the models)? 3. Usted below are the top 10 annual salaries in millions of dollars) of TV personalities. T 38 36 34 7 18 16 14 1 10.7 (a) Find the range of the sample data? (Round to one decimal places as needed.) 10.1 (b) Find the sample variance of the sample data? (Round to two decimal places as needed.) (C) Find the sample standard deviation of the sample data? (Round to two decimal places as needed.) 4. A certain group of test subjects had pulse rates with a mean of 73.8 beats per minute and a standard deviation of 10.8 beats per minute. Would it be unusual for one of the test subjects to have a pulse rate of 45.4 beats per minute? (a) What is the minimum "usual" value? (b) What is the maximum "usual" value? © Is 45.4 beats per minute an unusual pulse rate? Explain. 5. Below are 33 sorted ages of an acting award winner. 27 NA (a) Find the percentile corresponding to age 27. (Round to the nearest integer as needed.) (b) Find the value of the 35 percentile P 6. Blood platelet counts of women have a bell-shaped distribution with a mean of 280 and a standard deviation of 65, (All units are 1000 cells/AL.) What conclusion you can draw from empirical rule? 7. IQ sores have a mean of 100 and a standard deviation of 15. What can we conclude from Chebyshev's theorem? 8. Fourteen different second-year medical students at a hospital measured the blood pressure of the same person. The systolic readings (mm Hg) are listed below. 146 136 135 126 120 125 131 130 123 124 125 140 127 150 (a) Find the 5-number summary. (b) Construct a regular boxplot. 9. The following data representing tornadoes per year in Oklahoma from 1995 until 2004 to construct a modified box plot. 18 44 47 55 61 62 78 79 83 145 (a) Find the 5-number summary. (b) Find the lower outlier boundary and the upper outlier boundary. Find the outliers if exists (c) Find the minimum and maximum. Construct a modified boxplot.
Answer: c
Answer: a) To estimate the value of F,(10) using a central difference with h =...
Answer: a) To estimate the value of F,(10) using a central difference with h =...
Answer: a) To estimate the value of F,(10) using a central difference with h =...
Answer: a) To estimate the value of F,(10) using a central difference with h =...
Answer: c
Answer: C
Answer: a
Answer: D
Answer: a) To estimate the value of F,(10) using a central difference with h =...
Answer: D
Answer: C
Answer: D
Answer: c
Answer: V a) To estimate the value of F,(10) using a central difference with h...
11) The test scores of 32 students are listed in Problem 5. Find the third quartile, Q3 11) A) 80 C) 70 D) 99 B) 68 12) The test scores of 32 students are listed in Problem 5. Find first quartile, Q1 12) A) 32 D) 80 B) 56 C) 70 13) 13) The test scores of 32 students are listed in Problem 5. Find IQR= A) 43 C) 10 D) 38 B) 24 14) Compute the sample variance s2 =if a data set X- (X1, X2, X31 -(a, b, c) with, Variation of a --2, Variation of b-1, and Variation of c- 3, 14) D) 7 C) 14/3 A) 14 B) 0 15) if a data set X= (X1, X2, X3.X49 ). x=98, - 628. 15) Compute the sample variance s2 = D) 9 B) 2 C) 4 A) 3 with 16) (X1, X2, X3, X49 16) Compute the sample standard deviation, s= if a data set X x-98, 2- 628. C) 2 D) 4 B) 9 A) 3 End the mean of the data summarized in the given frequency distribution. 17) The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Find the Sample Mean waiting time (Weighted Average). Round your answer to one decimal place. 17) INumebr of Customers I Xmid = Waiting time (minutes) | fXmid = LL - UL 32 0 - 11 12 - 19 13 4. 20 - 27 D) 9.4 min C) 9.2 min. B) 7.0 min A) 13.5 min oblems 18 through 24, given a Whisker-and -Box Plot with values of its 5-number below: 7.7 8.7 5.5 18) Given a daat set of the weights (in pounds) of 30 newborn babies as X =(X1, X2, X3, ., X30) and 6.4 7.0 18) (%3D219. The Whisker-and-Box plot of the data set of the weights as shown in the figure above. Find Range = C) 2.3 D) 3.2 B) 1.3 A) 0.7 19) in pounds Given same information as one in Problem 18. Find the Variation of 8 %3D D) 0.7 C) -1.6 B) - 1.0 A) 1.0
Answer: B
Answer: A
Answer: a
Answer: ccccccccccccccccccccc
Answer: a) To estimate the value of F,(10) using a central difference with h =...
Answer: a) To estimate the value of F,(10) using a central difference with h =...
Answer: a) To estimate the value of F,(10) using a central difference with h =...
Answer: a) To estimate the value of F,(10) using a central difference with h =...
Answer: a) To estimate the value of F,(10) using a central difference with h =...
Answer: d
Answer: b
Answer: b
IS UULIU DES possib The quality control manager at a light bulb factory needs to estimate the mean We of a large shipment of light bulbs. The standard deviation is 117 hours. A random sample of 81 he bulbs indicated a sample meant of 420 hours. Complete parts (a) through (d) below a. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment. The 95% confidence interval estimate is from a lower limit of hours to an upper limit of hours. (Round to one decimal place as needed.) b. Do you think that the manufacturer has the right to state that the lightbulbs have a meanife of 470 hours? Explain Based on the sample at the manufacture the right to that the lightbulbs have a mean of 470 hours. Amen of 470 hours is standard errors the sample that the lights have a mean le of 470 hours e. Must you assume that the population light bulbife is normally distributed? Explain O A Yes the sample size is too large for the samping debution of the mean to be approximately normal by the Central Limit Theorem OB. N incs is known the sampling debution of the mean does not need to be approximately distributed OC. No, non s on and the same size is large enough the samping dibution of the mean is approximately by the Centra OD Yes the sample i s not large enough for the samping distribution of them to be mately normal by the Central Theorem Therom. d i? d. Suppose the and deviation changes to hours. What are your a The con t ervals would be from a lower hours to per hours Based on the same and a handard deviation of the manufacturer at the t eam ofrohousAman 470 standard Click to select your awer
Answer: a
Answer: B
Answer: D
Answer: b
A company claims that the mean of a population exceeds 120. A random sample is taken of size 225. It yielded a mean of 123 and a sample standard deviation of 25. Does the data support the company's claim at a level of significance of a = .05? What hypotheses could we use to test this claim? O Hoil = 120 Hoifi > 120 O Hoil = 120 Hoil < 120 O Hoil = 120 Hau 120 O Ho:ī = 225 Ho:Ẽ < 225 O How = 225 Ho:7 > 225 Since this scenario does not state the population distribution is normal, can we proceed with normal calculations? Yes, we can always assume the sampling distribution is Normal. O Yes, since np and n(1-p) is greater than 10, then the sampling distribution is approximately Normal. O Yes, since n is large (greater than 30), then the sampling distribution is approximately Normal. O No, we cannot use Normal Calculations. How can we calculate the p-value of the test statistic for this test? 120-123 25 V225 123-1 P(t> 13:120) 25 123-120 25 V 225 123-120 25 ✓225 pfectuara) 120-123 25 ✓225 What can conclusion can we make based on the p-value found in #3? O Since the p-value is greater than the significance level of 0.05, then we fail to reject the null. We do have convincing evidence that the population mean exceeds 120. Since the p-value is less than the significance level of 0.05, then we reject the null. We do not have convincing evidence that the population mean exceeds 120. O Since the p-value is greater than the significance level of 0.05, then we fail to reject the null. We do not have convincing evidence that the population mean exceeds 120. O Since the p-value is less than the significance level of 0.05, then we reject the null. We do have convincing evidence that the population mean exceeds 120.
Answer: D
Answer: C
stated that the mean time for a Chrysler Concorde to go from 0 to 60 miles per hour was 8.7 seconds. (b) The town of Leadville, Colorado, has an elevation over 10,000 feet. Suppose you wanted to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer in Leadville (because of less oxygen). What would you use for the alternate hypothesis? (c) Suppose you made an engine modification and you think the average time to accelerate from 0 to 60 miles per hour is reduced. What would you use for the alternate hypothesis? (d) For each of the tests in parts (b) and (c), would the -value area be on the left, on the right, or on both sides of the mean? ≈ 17.1. Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that the P/E ratio of a certain stock index is = 18. Let be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume that has a normal distribution and = 4.2. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? : = 18; :   < 18; left-tailed : ≠ 18; :   = 18; two-tailed      : = 18; :   > 18; right-tailed : = 18; :   ≠ 18; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that has a normal distribution with known .The Student's , since is large with unknown .     The Student's , since we assume that has a normal distribution with known .The standard normal, since we assume that has a normal distribution with unknown . What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find (or estimate) the -value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the -value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ? At the = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.     At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application.
Answer: a
Weatherwise is a Magarine published by the American Meteorological Society. One seglves a rating system used to cal Norester storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a Noraster is in progress at the severe storm class rating, Peak wave heights are usually measured from land (using binoculars) off fed cement pers. Suppose that a reading of 38 waves showed an average wave height of 16.7 feet. Previous studies of severe storms indicate that 3.5 feet. Does this information suggest that the storm is perhaps temporary increasing where the severe rating? Use a 0.01 (a) What is the level of significance? State the Ho! land alternate hypotheses > 16.4 16.4 My 16.4ft; ML 16.4ft Hot <16.4 16.4 ft Ny 16.4 : N1 Mo 16.4 ft Hol 16.4 lt; Note 16.4ft (b) What sampling distribution will you use? Explain the rationale for your choice of samping distribution The Student'st, since the sample seis large and known The Student's t, since the sample size is large and is unknown The standard normal, since the sample sue is large and is known The standard normal, since the sample stilarge and how What is the wate of the sample test (Round your answer to two de paes.) Estimate the value 0.100 0.050 0.010 P <0.250 <0.100 0 0.010 Sketch the sampling distribution and how the area carrosos Sketch the sampling distribution and show the area corresponding to the value A - - (a) Based on your answers in parts(a) to (c), will you reject or fail to reject the nu hypothesis? Are the data statistically significant at level a? At the a- 0.01 level, we reject the full hypothesis and conclude the data are statistically significant At the 0.01 level we reject the null hypothesis and conclude the data are not statistically significant At the a 0.01 level, we fato reject the nul nypothesis and conclude the data are statistical. ca At the 0.01 level, we fall to reject the null hypothesis and conclude the data are not statistically significant (e) Interpret your conclusion in the context of the application There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating There incent evidence at the 0.01 level to conclude that the mom inesing above the severe rating
Answer: a) To estimate the value of F,(10) using a central difference with h =...
Let x be a random variable that represents the pH of arterial plasma (le, acidity of the wood). For healthy adults, the mean of the x distribution 7.4.A new drug for arthritis has been developed However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that - 8.5 with sample standard deviations - 31. Use a % level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood (a) What is the level of cance? State the null and a ternate hypotheses Moi - 7AMM> 7.4 - Ng' 4 - 74, P A + A. Mou > 7.4; M = 7.4 74 7.4 MO! 7.4; 1 74 (b) What samping distribution will you use? Explain the rationale for your choice of aming der The standard normal, since the sample size is large and is known The Student'st, since the samplestre is large and is known The students, since the sample size is large and is unknown The standard normal, since the sample size is large and is unknown pe What is the value of the sample test statistic (Round your answer to three decals ) (c) Estimate the value. op value 0.250 0.100 < P-value < 0.250 -0.050 < valve < 0.100 0.010 < < 0.050 Palue <0.010 Sketch the samping distribution and show the area corresponding Sketch the sampling distribution and show the area corresponding to the value . (d) Based on your answers in parts (a) to (C), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? At the a 0.05 level we reject the null hypothesis and conclude the data are statistically significant At the 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant At the 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant At the a-0.05 level, we fall to reject the null hypothesis and conclude the data are not statistically significant (e) Interpret your conclusion in the context of the application There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood. There insufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood
Answer: a) To estimate the value of F,(10) using a central difference with h =...
≈ 17.1. Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that the P/E ratio of a certain stock index is = 18. Let be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume that has a normal distribution and = 4.2. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? : = 18; :   < 18; left-tailed : ≠ 18; :   = 18; two-tailed      : = 18; :   > 18; right-tailed : = 18; :   ≠ 18; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that has a normal distribution with known .The Student's , since is large with unknown .     The Student's , since we assume that has a normal distribution with known .The standard normal, since we assume that has a normal distribution with unknown . What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find (or estimate) the -value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the -value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?
Answer: a) To estimate the value of F,(10) using a central difference with h =...
A random sample of n - 16 communities in western Kansas gave the following information for people under 25 years of age. Xqt Rate of hay fever per 1000 population for people under 25 99 92 122 127 94 123 112 93 125 95 125 112 97 122 127 88 A random sample of 14 regions in western Kansas gave the following Information for people over 50 years old, Xg: Rate of hay fever per 1000 population for people over 50 94 109 102 96 110 110 79 115 100 89 114 8S 96 Use a calculator to calculate X, $1,, and sz. (Round your answers to two decimal places.) 0.05. (1) Assume that the hay fever rate in each age group has an approamately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use a (a) What is the level of significance? State the null and alternate hypotheses Ho - Mi Mi Mi 2 Hoi Ni - M H2 Ho - HH > 2 Ho! H H2 (b) What sampling distribution will you use? What assumptions are you making? The Student'st. We assume that both population distributions are approximately normal with unknown standard devations The standard normal. We assume that both population distributions are aproximately normal with n ow standard deviations The standard normal, we asume that both population distributions are approximately normal with new standard deviation The students. We assume that both population distributions are approximately normal with and deviation What is the value of the sample test statistic? (Test the difference - Round your answer to three decimal places) (c) Frd (or estimate the P-value Puve 0.250 0.125 Avue 0.250 0.050 < P-value < 0.125 0.025 < P ue < 0.050 0.005 < P-value < 0.025 S l ing distribution and show the area corresponding to the value (d) Based on your answers in parts (o) to (c), will you reject or fail to reject the hypothesis? Are the data statistically significant at level At the = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the e-0.05 level, we reject the us ypothesis and conclude the data are statistically w a nt At the a-0.05 level, we foto reject the null typothesis and conclude the data are statistically significant At the a= 0.05 level, we reject the nut hypothesis and conclude the data are not statistically cant. (e) Interpret your conclusion in the context of the application Fall to reject the null hypothesis, there is insuficient evidence that the moon rate of hayfever slower for the age group over 50 Par to repeat the press, there is wifest evidence that the mean role of the fewer is tower for e t group over 30 Reject the hypothes, there is sufficient evidence that the mean rate of Nayfever is for the age ou verso Reject the will hypothesis, there is incent evidence that the mean rate of h e r for the grader
Answer: a) To estimate the value of F,(10) using a central difference with h =...

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