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Statistics Assignment problems

1. The stem-and-leaf diagram below displays the number of vacation days taken in 1997 by a sample of40 employees of an electronics company.Stem Leaves0 00123334456889 Stem unit = ten1 0001111344562 00001234683 0014 3Referring to the stem-and-leaf display above, what PERCENTAGE of employees took 30 or more vacationdays?A. 10 B. 0.05 C. 5 D. 4 E. 0.10QUESTIONS #2 THROUGH #4 USE THE DATA GIVEN BELOW.A survey was taken to determine how much time UHD students spend doing homework per week. The random sample of UHD students resulted in the frequency distribution shown below.Time (in hours) Frequency0 and under 2 42 and under 4 64 and under 6 116 and under 8 188 and under 10 2610 and under 12 52. The class width is:A. 10.00 B. 2.00 C. 12.00 D. 1.99 E. 1003. What would be the APPROXIMATE shape of the frequency histogram?A. bell-shaped B. skewed to the right C. skewed to the leftD. bi-modal E. none of these4. What PERCENTAGE of the students studied less than 6 hours?A. 11 B. 70 C. 0.16 D. 30 E. 0.35. For a large survey of students, this graph would most likely describe:A. Students’ music preference (rock=0, opera=1)B. Students’ handed-ness (right=0, left=1)C. Students’ political partiesD. Students’ heights in inchesQUESTIONS #6 THROUGH #9 USE THE DATA GIVEN BELOW.A random sample of eleven college students were surveyed and asked what brand of laptop they use and how long the battery lasted after the last full charge:Laptop Brand: Samsung, Dell, HP, Apple, Dell, HP, Dell, Toshiba, Dell, HP, AppleBattery Life (hours): 9, 6, 4, 9, 6, 3, 8, 10, 9, 5, 8Assuming this data reflects all students:6. Assuming this data reflects all students at the college, what brand of laptop would you expect the averageor typical student to own?A. Samsung B. HP C. Toshiba D. Apple E. Dell7. A ____________ could be used to display the frequencies of the battery life data, and a ____________could be used to display the frequencies of the laptop brands.A. pie chart ; histogram B. bar chart ; stem-and-leaf displayC. histogram ; bar chart D. stem-and-leaf display ; histogramE. histogram; stem and leaf8. What would be the mean time the batteries lasted since the last full charge (in hours)?A. 9 B. 8 C. 7 D. 10 E. 7.59. The sample standard deviation of these battery lives, rounded to the nearest hundredth, would be:A. 2.32 B. 2.65 C. 7.00 D. 5.40 E. 2.22 QUESTIONS #10 THROUGH #13 REFER TO THE FOLLOWING EXCEL OUTPUT:Over the last 6 months, monthly returns (%) were tracked for 4 stock funds.FUND 1 FUND 2 FUND 3 FUND 4January 15 15 24 23February 12 13 15 24March 11 10 13 24April 18 5 9 24May 16 19 19 22June 11 10 13 25FUND 1 FUND 2 FUND 3 FUND 4Mean 13.83333333 12 15.5 23.66666667Standard Error 1.194896555 1.966384161 2.156385865 0.421637021Median 13.5 11.5 14 24Mode 11 10 13 24Standard Deviation 2.926886856 4.816637832 5.282045058 1.032795559Sample Variance 8.566666667 23.2 27.9 1.066666667Kurtosis -1.810019834 0.14343044 0.254750067 0.5859375Skewness 0.388189509 0.032215919 0.71453263 -0.665669013Range 7 14 15 3Minimum 11 5 9 22Maximum 18 19 24 25Sum 83 72 93 142Count 6 6 6 610. Which of these funds carries the most risk with respect to monthly returns?A. Fund 4 B. Fund 3 C. Fund 2 D. Fund 1 E. none of these11. Assuming an approximately normal distribution of return rates for Fund 4, we wouldexpect APPROXIMATELY 95% of the monthly return rates for Fund 4 to be in which of thefollowing intervals?A. (20.57 , 26.77) B. (22, 25) C. (22.63, 24.70) D. (23.25 , 24.07) E. (21.6 , 25.73)12. The 50th percentile of Fund 3’s monthly returns would be ________?A. 14 B. 15 C. 11.5 D. 13 E. 15.513. Consider the January monthly returns for Fund 1 and Fund 2. Relative to their own fund, which Januaryreturn had the better performance?A. They were the same B. Fund 1 C. Fund 2 D. cannot be determinedQUESTIONS #14 AND #15 USE THE TABLE GIVEN BELOW.The table contains the probability distribution for the number of televisions per household in the United States.X P(X)0 .081 .252 .383 .194 .085 .0214. What is the expected number of televisions per household?A. 2.0 B. 2.1 C. 2.5 D. 3.0 E. 2.815. What is the probability that a household has more than 2 televisions?A. 0.71 B. 0.67 C. 0.38 D. 0.33 E. 0.29QUESTIONS #16 AND #17 PERTAIN TO THE FOLLOWING:A study has shown that 30% of all students taking finance at Bellaire College fail the first exam. A random sample of 12 students taking finance at Bellaire College is selected.16. Find the probability that less than 5 students will fail the first finance exam.A. 0.1179 B. 0.1585 C. 0.2764 D. 0.7236 E. 0.882117. On average, how many students would you expect to fail the first finance exam?A. 8.4 B. 3.6 C. 1.5 D. 1.2 E. 1.9018. Determine P(-1.3 < Z < 0.16) for a standard normal distribution.A. 0.3396 B. 0.4668 C. -0.4668 D. -0.5332 E. 0.903219. The heights of women have a normal distribution with mean ? = 64 inches and VARIANCE of ?2 = 4 inches. Let X = height of a woman and find P(X < 65).A. 0.6915 B. 0.5000 C. 0.3085 D. 0.1915 E. none of theseQUESTIONS #20 THROUGH #22 PERTAIN TO THE FOLLOWING:The time to complete a set of homework problems has a normal distribution with mean 42 minutes andstandard deviation 9 minutes.20. Find the probability that a randomly selected student will complete the homework problems inless than 30 minutes.A. 0.9082 B. 0.4082 C. 0.4032 D. 0.133 E. 0.091821. One would expect 10% of students to complete their homework in more than ______ minutes.A. 55.0 B. 45.6 C. 43.4 D. 53.5 E. 1.2822. For a random sample of 36 students, find the probability that the SAMPLE MEAN completion time is greater than 45 minutes.A. 0.0228 B. 0.1293 C. 0.3707 D. 0.4772 E. 0.9772QUESTIONS #23 AND #24 PERTAIN TO THE FOLLOWING:A travel agent would like to estimate confidence intervals for the average price of a hotel room during the summer in a resort community. The agent takes a random sample of 16 hotels from the community, and finds that the mean price of regular room is $115 with a sample standard deviation of $30. Assume the population of prices is normally distributed.23. Find the lower bound (to the nearest hundredth) for a 95% confidence interval for µ.A. 113.13 B. 102.66 C. 101.85 D. 100.30 E. 99.0224. Suppose a 90% confidence interval for µ is (108, 122). State which of the following is a correctinterpretation of the confidence interval by completing the following: We are 90% confident that_______A. the average price for regular room for the 16 hotels is between $108 and $122.B. the average price for regular room for all hotels in the community is between $108 and $122.C. the price for regular room for the 16 hotels is between $108 and $122.D. the price for regular room for all hotels in the community is between $108 and $122.25. A study is being planned to estimate the mean number of inches that trees will grow per year in a forest.From previous studies, it is known that the growth is normally distributed and the population standarddeviation is 0.80 inches. The analysts wish to have 90% confidence and want the estimate to be within0.20 inch. What size sample is needed for this study?A. 44 B. 43.30 C. 43 D. 27 E. 726. An educator is interested in the average amount of time that children watch television. Fifteen childrenwere randomly sampled and the amount of time spent (in hours) watching TV per week is obtained.Use the printout below to answer the following question:TIME (hours)15 TIME SPENT WATCHING TV5 7 Mean 9.86666670 Standard Error 1.4470559 Median 1014 Mode 510 Standard Deviation 5.604425 Sample Variance 31.40952411 Kurtosis -0.16105421 Skewness 0.070196116 Range 2112 Minimum 013 Maximum 218 Sum 1482 Count 15Confidence Level(90.0%) 2.5487127Find the upper bound (to the nearest hundredth) of the 90% confidence interval for µ.A. 12.70 B. 12.42 C. 11.31 D. 11.81 E. 2.5527. A patient is tested for TB at a medical clinic. Consider the hypotheses:Ho: The patient does not have TB Ha: The patient has TBWhen does a Type I error occur?A. The test gives a negative result (the patient does not have TB) when the patient actually has TBB. The test gives a negative result (the patient does not have TB) when the patient does not have TBC. The test gives a positive result (the patient has TB) when the patient actually has TBD. The test gives a positive result (the patient has TB) when the patient does not have TBQUESTIONS #28 THROUGH #31 PERTAIN TO THE FOLLOWING:An economist claims that the average Hispanic owned business generates revenues of less than $70,000 annually. A random survey of 10 Hispanic owned businesses revealed an average annual revenue of $58,600 with a standard deviation of $18,000. Assume a normal population. We wish to test the economist's claim, at a 10% significance level.28. State the null and alternative hypotheses for the test.A. H0: ? ? 58,600 Ha: ? > 58,600B. H0: ? = 58,600 Ha: ? ? 58,600C. H0: ? > 70,000 Ha: ? ? 70,000D. H0: ? ? 70,000 Ha: ? < 70,000E. H0: ? = 70,000 Ha: ? ? 70,00029. Calculate the value of the test statistic.A. -2.003 B. -0.633 C. 2.003 D. 1.372 E. 1.28230. We would reject Ho if the test statistic is:A. less than -1.383 B. less than -1.28 C. less than -1.372 D. greater than 1.383E. greater than 1.64531. Based on the data and this hypothesis test, state the conclusion at a 10% level of significance.A. There is sufficient evidence that the average annual revenue for Hispanic owned businesses is $70,000.B. There is sufficient evidence that the average annual revenue for Hispanic owned businesses is more than $70,000.C. There is sufficient evidence that the average annual revenue for Hispanic owned businesses is less than $70,000.QUESTIONS #32 THROUGH #33 PERTAIN TO THE FOLLOWING:A market research analyst believes that the average weekly household expenditure on groceries in Pearland is $125. Assume that the weekly household expenditures are normally distributed. In setting up the hypotheses to test the analyst’s belief, she obtained a test statistic value of z = 1.4532. Calculate the p-value based on normal distribution.A. 0.4265 B. 0.1470 C. 0.0287 D. 0.0735 E. 0.057433. Based on the results of the hypothesis test at the 10% level of significance, which of the following is a correct conclusion?A. There is sufficient evidence to conclude that the average weekly household expenditure on groceries in Pearland is $125.B. There is not sufficient evidence to conclude that the average weekly household expenditure on groceries in Pearland is significantly different from $125.C. There is sufficient evidence to conclude that the average weekly household expenditure on groceries in Pearland is significantly different from $125.QUESTIONS #34 AND #35 PERTAIN TO THE FOLLOWING:An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. Some results from a simple linear regression of SALARY versus GMAT are shown below.34. Predict the starting salary for a graduate who scored a 650 on the GMAT.A. $92,040 B. $56,160 C. $59,826 D. $66,70035. Set up the null and alternative hypotheses for testing whether GMAT is a useful predictor of SALARY.A. Ho: ?1 = 228 vs. Ha: ?1 ? 228 B. Ho: ?1 = 0 vs. Ha: ?1 ? 0C. Ho: ?1 ? 0 vs. Ha: ?1 > 0 D. Ho: ?1 = 228 vs. Ha: ?1 = 228QUESTIONS #36 THROUGH #40 REFER TO THE FOLLOWING:A professor wants to analyze the number of hours students spent online during the weekend and their scores on a test the following Monday. Part of the regression output appears below.Coefficients Standard Error t Stat P-valueIntercept 93.97 4.52 2.77 0.050693Hours Online -4.07 0.86 -4.73 0.008048R Square 0.69105342 36. Interpret the SLOPE of the least squares line.A. For every additional hour spent online, the predicted test score increases by 93.97 points, on average.B. For every additional hour spent online, the predicted test score decreases by 4.07 points, on averageC. For every additional hour spent online, the predicted test score increases by 4.52 points, on average.D. For every 1 point increase in test score, the predicted time spent online decreases by 4.07 hrs, on averageE. For every 1 point increase in test score, the predicted time spent online increases by 93. min. on average.37. Determine the value of the test statistic that the manager used to test whether test score is a usefulpredictor of performance.A. -4.73 B. 4.52 C. 93.97 D. 2.77 E. -4.0738. At the .05 level, the professor could conclude that the time spent online by students over the weekend is auseful predictor of test scores the following Monday.A. TRUEB. FALSE39. What is the least squares regression equation?A. B.C. D.40. _________________is the percentage of variation in performance explained by test score.A. 93.974% B. 86% C. 4.07% D. 69.11% E. 0.69%

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