Statistics I

Northcentral University Data File 3/Statistics in Educational Research Data File 3 Show all work Chapter Five 1) If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours? Answer : According to the 68-95-99.7:  Approximately 68% of light bulbs have a life between µ-σ = 2000 and µ+σ = 3000 (where µ is the mean and σ is the standard deviation)  Approximately 95% of light bulbs have a life between µ-2σ = 1500 and µ+2σ = 3500  Approximately 99.7% of light bulbs have a life between µ-3σ = 1000 and µ+3σ = 4000 Therefore, (99.7%)/2= 49.85% of light bulbs have a life inferior to 2500 (which is the mean) This result can be verified by using z score tables. Indeed, µ=2500 and σ = 500 For the value 2500 hours, Z score = = 0. The z score table reveals that the corresponding percentile is 50%. Thus, 50% of light bulbs have a life less than 2500 hours Department Page 1 of 7 © 2011 Northcentral University djenny:02112011 10000 E. University Dr, Presco Valley, AZ 86314 USA www.ncu.edu p: 928-541-7777 f: 928-541-7817 Northcentral University Data File 3/Statistics in Educational Research 2) The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of bulbs has lifetimes that lie within 1 standard deviation of the mean on either side? Answer : µ = 370 hours and σ = 5 hours. According to the 68-95-99.7 rule, approximately 68% of light bulbs have a life within 1 standard deviation of the mean(µ) on either side, which is between µ-σ = 365 hours and µ+σ = 375 hours. This result can be verified by using z score tables.  Indeed, For the value µ+σ= 375, Z score = = = 1 The z score table reveals that the corresponding percentile is 84.13%.  For the value µ-σ = 365, Z score = = = -1 The z score table reveals that the corresponding percentile is 15.87% Thus, the percent of all scores that fall between µ-σ and µ+σ is (84.13 -15.87) = 68.26% 3) The amount of Jen’s monthly phone bill is normally distributed with a mean of $60 and a standard deviation of $12. Fill in the blanks: 68% of her phone bills are between $______________ and $______________. Answer : µ= $60 and σ = $12 68% of her phone bills are between µ-σ= $48 and µ+σ= $72 4) The amount of Jen’s monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25 th percentile. Answer: The Z score tables reveal us that for an area of 0.25, the corresponding value of Z is -0.67. Also, Z score = So, Value = = -0.67x10 + 50 = $43.30 25th percentile = $43.30 Department Page 2 of 7 © 2011 Northcentral University djenny:02112011 10000 E. University Dr, Presco Valley, AZ 86314 USA www.ncu.edu p: 928-541-7777 f: 928-541-7817

BTM7 | 104-8 | Statistics I | lab | Northcentral University Data F

Northcentral University Data File 2/Statistics in Educational Research Data File 2 Chapter Three (Show all your work) 1) A teacher asked each of her students how many novels they had read in the previous six months. The results are shown below. 0 1 5 4 2 1 3 2 2 7 2 5 0 1 0 1 1 2 6 0 2 3 1 2 7 1 4 2 3 1 7 0 0 2 1 1 0 6 1 7 Construct a frequency table for the number of novels read. Number Frequency 0 7 1 11 2 9 3 3 4 2 5 2 6 2 7 4 2) The frequency table shows the weights in ounces of 30 stones Weight (oz) Number of Stones 1.2-1.6 5 1.7-2.1 2 2.2-2.6 5 2.7-3.1 5 3.2-3.6 13 Use the above information to construct a cumulative frequency table for the data. Department Page 1 of 7 © 2011 Northcentral University djenny:02112011 10000 E. University Dr, Presco Valley, AZ 86314 USA www.ncu.edu p: 928-541-7777 f: 928-541-7817 Northcentral University Data File 2/Statistics in Educational Research Weight 1.2-1.6 1.2-2.1 1.2-2.6 1.2-3.1 1.2-3.6 Number of Stones 5 7 12 17 30 3) Use the following data to construct a bar chart. Job categories Clerical Management Maintenance Professional Unemployed 5 4 6 2 1 Create a bar graph and place the above data in a bar graph. 4) The data below are the numbers of hours of homework done as reported by 24 high school juniors for the last week in September 2006. 6, 5, 6, 4, 6, 6, 9, 7, 6, 3, 8, 5, 5, 8, 6, 5, 8, 6, 5, 7, 5, 8, 7, 4 Create a histogram using the above data. Use bin width (size of the bar) of 2 hours. Department Page 2 of 7 © 2011 Northcentral University djenny:02112011 10000 E. University Dr, Presco Valley, AZ 86314 USA www.ncu.edu p: 928-541-7777 f: 928-541-7817 Northcentral University Data File 2/Statistics in Educational Research 5) Examine the stem and leaf plot below. Find the original data from the stem and leaf plot. Stem Leaves 1 1,8 6 2 1,1,3,7 3 1,3,3,8,9 4 3,4 Answer: 11, 18, 16, 21, 21, 23, 27, 31, 33, 33, 38, 39, 43, 44 6) Create a stem and leaf plot with the following data. 10, 12, 33, 25, 22, 18, 19, 31, 28, 22, 13, 15, 15, 20, 21, 35, 32 Stem Leaves 1 2 3 0, 2, 3, 5, 5, 8, 9 0, 1, 2, 2, 5, 8 1, 2, 3, 5 Department Page 3 of 7 © 2011 Northcentral University djenny:02112011 10000 E. University Dr, Presco Valley, AZ 86314 USA www.ncu.edu p: 928-541-7777 f: 928-541-7817 Northcentral University Data File 2/Statistics in Educational Research Chapter Four (Show all your work) 1) The students of Hugh Logan’s math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean score. 552 593 358 352 537 349 357 596 470 482 Mean = (552+593+358+352+537+349+357+596+470+482)/10=464.6 Mean=464.6 2) The salaries of ten randomly selected physicians are shown below. Find the median salary. $105,000 $149,000 $163,000 $214,000 $225,000 $116,000 $111,000 $791,000 $240,000 $178,000 $105,000; $111,000; $116, 000; $149,000; $163, 000 ; $178, 000 ; $214,000; $225,000; $240,000; $791,000 Median = ($163,000+$178,000)/2=$170500 Median=$170,500 3) Find the mode(s) for the given sample data. 20, 43, 46, 43, 49, 43, 49 20, 43, 43, 43 , 46, 49, 49 Mode = 43 4) The mathematics SAT scores of the seven students in a mathematics seminar are 533, 553, 578, 586, 619, 626, and 633. Suppose that the student with the score of 533 drops the seminar and is replaced by a student with a score of 765. What will happen to the mean and the median scores of the class? Explain. Answer : Both the median and the mean will increase. Indeed, For {533, 533, 578, 586 , 619, 626, 633} Median = 586 Mean = (533+533+578+586+619+626+633)/7= 586.86 Department Page 4 of 7 © 2011 Northcentral University djenny:02112011 10000 E. University Dr, Presco Valley, AZ 86314 USA www.ncu.edu p: 928-541-7777 f: 928-541-7817

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