Statistical Problem Solving: Frequency Distributions & Analysis

QUESTION 1 1. Use the given frequency distribution to find the: 1. class width: 2. class midpoint of the first class: 3. class boundaries of the first class: 3 points QUESTION 2 1. The weight (in pounds ) of 30 preschool children are listed below. Find the five-number summary. 25 25 26 26.5 27 27 27.5 28 28 28.5 29 29 30 30 30.5 31 31 32 32.5 32.5 33 33 34 34.5 35 33 37 37 38 38 The five number summary is: Min = , Q1 = , Med = , Q3 = , Max = 4 points QUESTION 3 1. The ages (in years) of 25 people are listed below: 38 43 55 65 66 68 70 73 74 76 80 82 87 90 99 Use the data above to identify any outlier(s). Write your answers in order separated by comma if needed. 1 points

QUESTION 4 1. The mean math score is 73, with a standard deciation of 4. Use the Empirical Rule to determine what percent of the scores lie between 69 and 77. ( Assume the data set has a bell-shaped distribution.) 1 points QUESTION 5 1. Provide an appropriate response. Determine the probability distribution's missing value. The probability that a tutor will see 0, 1, 2, 3, or 4 students 1 points QUESTION 6 1. For the mathematics past of the ACT the mean is 20.6 with the standard deviation of 5.1, and for the mathematics part of the SAT the mean is 514 with a standard deviation of 113. JR scores a 27 on the ACT and 660 on the SAT. Use z-score to determine on which test he performed better. SAT ACT Both scores have the same relative position 1 points QUESTION 7 1. Provide an appropriate response. SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests while a junior and scores 1130 on the SAT and 25 on the ACT. Compare the scores. A score of 25 on the ACT test was better. You cannot determine which score is better from the given information. A score of 1130 on the SAT test was better. The two scores are statistically the same.

1 points QUESTION 8 1. Provide an appropriate response. In a pizza takeout restaurant, the following probability distribution was obtained. The random variable x represents the number of toppings for a large pizza. Find the mean and standard deviation. mean: 1.30; standard deviation: 2.38 mean: 1.04; standard deviation: 1.14 mean: 1.14; standard deviation: 1.04 mean: 1.30; standard deviation: 1.54 1 points QUESTION 9 1. Provide an appropriate response. Use the Standard Normal Table to find the probability. The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. Find the probability of a pregnancy lasting more than 300 days. 0.237 5 0.318 9 0.016 0.983 4 1 points QUESTION 10

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1. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a member selected at random is from the shaded area of the graph. Round answer to four decimal places. 1 points QUESTION 11 1. Find the z-score that corresponds to the given area under the standard normal curve. Round answers to two decimal places. 1 points QUESTION 12 1. Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution. The monthly rents for studio apartments in a certain city have a mean of $980 and a standard deviation of $170. Random samples of size 50 are drawn from the population and the mean of each sample is determined.

$980, $3.40 $138.59, $24.04 $138.59, $170 $980, $24.04 1 points QUESTION 13 1. Assume the sample is taken from a normally distributed population and construct the indicated confidence interval. A random sample of 16 men have a mean height of 67.5 inches and a standard deviation of 3.7 inches. Construct a 99% confidence interval for the population standard deviation, σ. (2.5, 6.7) (1.3, 3.5) (2.6, 6.3) (2.6, 6.9) 1 points QUESTION 14 1. Provide an appropriate response. Find the critical values, and , for c = 0.99 and n = 10. 1.735 and 23.589 2.156 and 25.188 2.088 and 21.666 2.558 and 23.209 1 points QUESTION 15

1. Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. In a random sample of 26 computers, the mean repair cost was $169 with a standard deviation of $36. < < 2 points QUESTION 16 1. Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol ( μ, ρ, σ ) for the indicated parameter. A psychologist claims that more than 5.8 percent of the population suffers from professional problems due to extreme shyness. Use p , the true percentage of the population that suffers from extreme shyness. H 0 : p = 5.8% H 1 : p ≥ 5.8% H 0 : p = 5.8% H 1 : p > 5.8% H 0 : p = 5.8% H 1 : p ≤ 5.8% H 0 : p = 5.8% H 1 : p < 5.8% 1 points QUESTION 17 1. Express the null hypothesis and the alternative hypothesis in symbolic form for a test to support this claim. Use the correct symbol for the indicated parameter. The owner of a football team claims that the average attendance at games is over 68,800, and he is therefore justified in moving the team to a city with a larger stadium. H 0 : μ = 68,800 H 1 : μ > 68,800 H 0 : μ < 68,800 H 1 : μ ≥ 68,800

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H 0 : μ = 68,800 H 1 : μ < 68,800 H 0 : μ > 68,800 H 1 : μ ≤ 68,800 1 points QUESTION 18 1. Express the null hypothesis and the alternative hypothesis in symbolic form for a test to support this claim. Use the correct symbol for the indicated parameter. A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the σ = 3.3 mg claimed by the manufacturer. H 0 : σ ≤ 3.3 mg H 1 : σ > 3.3 mg H 0 : σ ≠ 3.3 mg H 1 : σ = 3.3 mg H 0 : σ ≥ 3.3 mg H 1 : σ < 3.3 mg H 0 : σ = 3.3 mg H 1 : σ ≠ 3.3 mg 1 points QUESTION 19 1. Find the critical value or values of χ 2 based on the given information. H 1 : σ < 0.14 n = 23 α = 0.10 14.04 2 - 30.81 3 30.81 3 14.84

8 1 points QUESTION 20 1. Provide an appropriate response. The mean age of bus drivers in Chicago is 48.7 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis? There is not sufficient evidence to reject the claim μ = 48.7. There is not sufficient evidence to support the claim μ = 48.7. There is sufficient evidence to reject the claim μ = 48.7. There is sufficient evidence to support the claim μ = 48.7. 1 points QUESTION 21 1. Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is μ d = 0. Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed. t = - 1.185 t = - 0.690 t = - 1.480 t = - 0.523 1 points QUESTION 22 1. Express the alternative hypothesis in symbolic form. A professor claims that the mean amount of time (in hours) sophomores spent studying for the statistics final exam is more than that of freshmen. Assume that the two samples are independent. Let the freshmen be the first population and the sophomores be the second population.

H a : μ 1 < μ 2 H a : μ 1 > μ 2 H a : μ 1 = μ 2 H a : μ 1 ≠ μ 2 1 points QUESTION 23 1. At a local college, 65 female students were randomly selected and it was found that their mean monthly income was $ 603 with a population standard deviation of $121.50. Seventy-five male students were also randomly selected and their mean monthly income was found to be $ 645 with a population standard deviation of $168.70. Test the claim that female students have a lower monthly income than male students. Use α = 0.01. The critical values (x): (round to two decimal places and separate your answers with comma if needed) The test statistics is (round to two decimal places) Decision: (Type either "Reject the null" or "Fail to reject the null".) 3 points QUESTION 24 1. A trucking firm suspects that the variance for a certain tire is greater than 1,000,000. To check the claim, the firm puts 101 of these tires on its trucks and gets a standard deviation of 1200 miles. If α = 0.05, test the trucking firm's claim using P-values. The degrees of freedom (df): Test statistic: P - value : (round to four decimal places) Decision: (type "Reject the null" or "Fail to reject the null") Interpretation: At 5% significance level, there is suffient evidence to support the firm's claim. (Type "agree" or "disagree") 5 points QUESTION 25 1. Construct the indicated confidence interval for the difference between the two population means. Assume that the two

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samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. A paint manufacturer wished to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Construct a 98% confidence interval for the difference between the mean drying time for paint of type A and the mean drying time for paint of type B. 8.48 hrs < μ 1 - μ 2 < 19.12 hrs 8.25 hrs < μ 1 - μ 2 < 19.35 hrs 8.19 hrs < μ 1 - μ 2 < 19.41 hrs 8.32 hrs < μ 1 - μ 2 < 19.28 hrs 1 points QUESTION 26 1. Find the value of the linear correlation coefficient r . The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Cost 9 2 3 4 2 5 9 10 Number 85 52 55 68 67 86 83 73 2. 3. Round your answer to three decimal places. 4. 1 points QUESTION 27 1. Provide an appropriate response. The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. Find the equation of the regression line for the given data.

= -2.755x + 96.139 = -96.139x + 2.755 = -2.755x - 96.139 = 96.139x - 2.755 1 points QUESTION 28 1. Provide an appropriate response. Given the equation of a regression line is = -1.5x- 1.8, what is the best predicted value for y given Assume that the variables x and y have a significant correlation. Round your answer to two decimal places. 1 points Click Save and Submit to save and submit. Click Save All Answers to save all answers.

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