Final Partial Review #2 Stats Key2

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College of Coastal Georgia *

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1401

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Statistics

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Apr 3, 2024

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Uploaded by savannahechesser

Final Partial Review #2 (Answer Key) Also Study Final Partial Review #1 and the activities (except Chapter 9 would be only for a bonus problem or problems)! 1. Determine whether the statement describes a population or a sample. The heights of 5 out of the 32 okra plants at Mr. Lonardo's greenhouse. A) Population B) Sample 2. Months of the year are an example of which type of data? A) Extreme B) Quantitative C) Statistic D) Qualitative 3. An experiment in which only the subject does not realize whether they have been placed in the experimental or control group is ____. A) single-blind B) double-blind 4. Results sometimes produce flawed conclusions which can be a form of ____.

A) Bias B) Participation Bias C) Researcher Bias D) Processing Error(s) E) Dropout F) Nonadherent(s) 5. Consider the following frequency table representing the distribution of hours students study for an exam in a week. Hours Students Study for an Exam in a Week Hours Frequency 4 14 5 2 6 12 7 3 8 11 Determine the mean and standard deviation for the study. A) 𝑥̅ = 5.8, ? = 1.6 B) 𝑥̅ = 5.9, ? = 1.6 C) 𝑥̅ = 5.9, ? = 1.7 D) 𝑥̅ = 6.1, ? = 1.7 6. The following bar graph represents the number of dogs and cats treated by a local vet during one week.

Step 1. Were there more dogs or more cats treated during the week? A) More dogs were treated during the week than cats. B) More cats were treated during the week than dogs. C) The number of dogs treated equals the number of cats treated. Step 2. On which day was the greatest total number of cats and dogs treated? A) Monday B) Tuesday C) Wednesday D) Thursday E) Friday

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7. Select the graph that best illustrates the following distribution shape: Uniform 8. Consider the following data. 11, −9, 9, −14, 14, 1 Step 1. Determine the mean of the given data. Answer: _______________ Step 2. Determine the median of the given data. Answer: _______________ Step 3. Determine if the data set is unimodal, bimodal, multimodal, or has no mode. Identify the mode(s), if any exist. Answer: __________

9. Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 16, 12, 17, 8, 15, 15, 10, 11, 19, 18 Answer: Range: _______________ Population Variance: _______________ Population Standard Deviation: _______________ 10. Consider the following box plots for Data Set A and Data Set B. Step 1. Which data set has the largest value? A) Data Set A B) Data Set B Step 2. Which data set has the largest variation?

A) Data Set A B) Data Set B 11. There are 725 identical plastic chips numbered 1 through 725 in a box. What is the probability of reaching into the box and randomly drawing the chip numbered 548 ? Express your answer as a simplified fraction or a decimal rounded to four decimal places. Answer: _______________ 12. A box contains 19 large marbles and 18 small marbles. Each marble is either green or white. 9 of the large marbles are green, and 8 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or green? Express your answer as a fraction or a decimal number rounded to four decimal places. Answer: _______________

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13. Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a queen and then, without replacement, a king? Express your answer as a fraction or a decimal number rounded to four decimal places. Answer: _______________ 14. A coordinator will select 5 songs from a list of 9 songs to compose an event's musical entertainment lineup. How many different lineups are possible? Answer: _______________ 15. Consider the following data: 𝐱 0 1 2 3 4 𝐏(𝑋 = 𝑥) 0.1 0.3 0.1 0.2 0.3 Step 1. Find the expected value 𝐸( 𝑋 ) . Round your answer to one decimal place. Answer: _______________ Step 2. Find the variance. Round your answer to one decimal place. Answer: _______________ Step 3. Find the standard deviation. Round your answer to one decimal place. Answer: _______________ Step 4. Find the value of 𝑃(𝑋 > 2) . Round your answer to one decimal place.

Answer: _______________ Step 5. Find the value of 𝑃(𝑋 ≥ 4) . Round your answer to one decimal place. Answer: _______________ 16. A certain insecticide kills 80% of all insects in laboratory experiments. A sample of 12 insects is exposed to the insecticide in a particular experiment. What is the probability that every insect will die? Round your answer to four decimal places. Answer: _______________ 17. The auto parts department of an automotive dealership sends out a mean of 8 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 3 ? Round your answer to four decimal places. Answer: _______________ 18. Given 𝑋 = 80.6 , 𝜇 = 75.1 , and 𝜎 = 2.1 , indicate on the curve where the given 𝑋 value would be.

19. Find the area under the standard normal curve to the left of 𝑧 = −1.15 . Round your answer to four decimal places, if necessary. Answer: ____________________ 20. The time spent waiting in the line is approximately normally distributed. The mean waiting time is 4 minutes and the variance of the waiting time is 1 . Which of the following probabilities is the largest? A) P(X>5) B) P(4<X<6) C) P(X=4) D) P(X<5) 21. Find the value of 𝑧 such that 0.1 of the area lies to the left of 𝑧 . Round your answer to two decimal places. Answer: ____________________ 22. Decide if the statement is True or False. A sampling distribution of sample means has a standard deviation equal to the population standard deviation, 𝜎 .

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A) True B) False 23. Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.3 and a mean diameter of 208 inches. If 60 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.1 inches? Round your answer to four decimal places. Answer: _______________ 24. A marketing research company desires to know the mean consumption of milk per week among people over age 45 . A sample of 306 people over age 45 was drawn and the mean milk consumption was 3.9 liters. Assume that the population standard deviation is known to be 0.7 liters. Construct the 98% confidence interval for the mean consumption of milk among people over age 45 . Round your answers to one decimal place. Answer: Lower endpoint: _______________ Upper endpoint: _______________ 25. Consider the value of ? such that the area under the curve between − ⃒ ? ⃒ and ⃒ ? ⃒ equals 0.99 . Step 1. Select the graph which best represents the given description of ? .

Step 2. Assuming the degrees of freedom equals 30 , select the ? value from the ? table. Answer: ____________________ 26. Wildlife conservationists studying grizzly bears in the United States found that the mean weight of 27 adult males was 601 pounds with a standard deviation of 85 pounds. Construct a 98% confidence interval for the mean weight of all adult male grizzly bears in the United States. Assume that the weights of all adult male grizzly bears in the United States are normally distributed. Round to the nearest whole number. Answer: Lower endpoint: _______________ Upper endpoint: _______________

27. The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 44 who smoke. Step 1. Suppose a sample of 632 Americans over 44 is drawn. Of these people, 462 don't smoke. Using the data, estimate the proportion of Americans over 44 who smoke. Enter your answer as a fraction or a decimal number rounded to three decimal places. Answer: _______________ Step 2. Suppose a sample of 632 Americans over 44 is drawn. Of these people, 462 don't smoke. Using the data, construct the 90% confidence interval for the population proportion of Americans over 44 who smoke. Round your answers to three decimal places. Answer: Lower endpoint: _______________ Upper endpoint: _______________ 28. A survey of 147 randomly selected students at one college showed that only 83 checked their campus email account on a regular basis. Construct a 98% confidence interval for the percentage of students at the college who do not check their email account on a regular basis. Round to one decimal place. Answer: Lower endpoint: _______________ Upper endpoint: _______________ 29. A newsletter publisher believes that over 68% of their readers own a personal computer. Is there sufficient evidence at the 0.02 level to substantiate the publisher's claim? State the null and alternative hypotheses for the above scenario. Answer: 𝐻 0 : _______________ 𝐻 𝑎 : _______________

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30. A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 427 gram setting. It is believed that the machine is underfilling the bags. A 32 bag sample had a mean of 421 grams. Assume the population variance is known to be 576 . A level of significance of 0.02 will be used. State the null and alternative hypotheses. Answer: 𝐻 0 : _______________ 𝐻 𝑎 : _______________ 31. A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 407 gram setting. It is believed that the machine is underfilling the bags. A simple random sample of 9 bags has results below. Assume the population distribution is approximately normal. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. 406.2 406.5 406.7 406.8 406.9 406.9 407.0 407.0 407.1 Test the claim at the 0.025 significance level. A) H o : the mean weight of the bags equals 407 grams. H 1 : the mean weight of the bags does not equal 407 grams. Test statistic Z = -2.2238 and P value = 0.0568 Conclusion: we should reject the null hypothesis B) H o : the mean weight of the bags equals 407 grams. H 1 : the mean weight of the bags is less than 407 grams. Test statistic T = -2.2238 and P value = 0.0284 Conclusion: we should fail to reject the null hypothesis C) H o : the mean weight of the bags equals 407 grams. H 1 : the mean weight of the bags is less than 407 grams. Test statistic T = -2.2238 and P value = 0.0284 Conclusion: we should reject the null hypothesis D) H o : the mean weight of the bags equals 407 grams. H 1 : the mean weight of the bags is less than 407 grams. Test statistic Z = -2.2238 and P value = 0.0284 Conclusion: we should fail to reject the null hypothesis

32. Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship. The age of a vehicle and cost of maintenance A) Positive B) Negative C) No correlation 33. Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars. 𝐸??𝑖?𝑎??? 𝑆𝑎??? 𝑉????? = 46.63 + 0.47(𝐴?????𝑖?𝑖?𝑔 𝐸𝑥????𝑖?????) If the company has a target sales volume of $275,000 , how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar. Answer: $ _______________

1. Correct Answer: Sample 2. Correct Answer: Qualitative 3. Correct Answer: single-blind 4. Correct Answer: Bias 5. Correct Answer: (b) 𝑥̅ = 5.9, ? = 1.6 6. Step 1.Correct Answer: More cats were treated during the week than dogs. Step 2.Correct Answer: Thursday 7. Correct Answer: 8. Step 1.Correct Answer: 2 Step 2.Correct Answer: 5 Step 3.Correct Answer: No Mode 9. Correct Answer: Range: 11 , Population variance: 12.1 , Population standard deviation: 3.5 10. Step 1.Correct Answer: Data Set A Step 2.Correct Answer: Data Set B 11. Correct Answer: 1 725 or 0.0014 12. Correct Answer: 27 37 or 0.7297 13. Correct Answer: 4 663 or 0.0060 14. Correct Answer: 15120 15. Step 1.Correct Answer: 2.3 Step 2.Correct Answer: 2.0 Step 3.Correct Answer: 1.4

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Step 4.Correct Answer: 0.5 Step 5.Correct Answer: 0.3 16. Correct Answer: 0.0687 17. Correct Answer: 0.0286 18. Correct Answer: 19. Correct Answer: 0.1251 20. Correct Answer: D) P(X<5) 21. Correct Answer: −1.28 22. Correct Answer: False 23. Correct Answer: 0.4514 24. Correct Answer: Lower endpoint: 3.8 Upper endpoint: 4.0 25. Step 1.Correct Answer:

Step 2.Correct Answer: 2.750 26. Correct Answer: Lower endpoint: 560 Upper endpoint: 642 27. Step 1.Correct Answer: 0.269 Step 2.Correct Answer: Lower endpoint: 0.240 Upper endpoint: 0.298 28. Correct Answer: Lower endpoint: 34.0 Upper endpoint: 53.1 29. Correct Answer: 𝐻 0 : ? = 0.68 , 𝐻 𝑎 : ? > 0.68 30. Correct Answer: 𝐻 0 : 𝜇 = 427 𝐻 𝑎 : 𝜇 < 427 31. Correct Answer: B H o : the mean weight of the bags equals 407 grams. H 1 : the mean weight of the bags is less than 407 grams. Test statistic T = -2.2238 and P value = 0.0284 Conclusion: we should fail to reject the null hypothesis 32. Correct Answer: Positive 33. Correct Answer: $485,894

Final Partial Review #2 Stats Key2

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