6. (6 pts) A tech service hot line call center is concerned about the duration o
ID: 3129872 • Letter: 6
Question
6. (6 pts) A tech service hot line call center is concerned about the duration of inbound calls. You have been tasked with compiling and analyzing the center's call data, below, representing a sample of a day's inbound call volume. (Sec 3.5.6-3.5.7) Customer ID Call date Call duration 125260805 10/1/2010 32 a. Calculate the sample mean and standard deviation for call duration time. 125265384 10/1/2010 163 125266412 10/1/2010 7 125267836 10/1/2010 29 125281795 10/1/2010 84 125282733 10/1/2010 60 125284950 10/1/2010 36 b. Calculate a 95% confidence interval for the mean call duration 125286575 10/1/2010 76 from the sample data. 125292230 10/1/2010 85 125300266 10/1/2010 52 125306688 10/1/2010 39 125311602 10/1/2010 101 125313493 10/1/2010 194 125316250 10/1/2010 283 c. Six months ago, the average call duration was 126. Using your 125320565 10/1/2010 173 confidence interval, test the hypothesis that the current average 125323846 10/1/2010 88 call duration for the entire call center is unchanged from 6 months 125329947 10/1/2010 61 ago, at 95% confidence. (Be sure to state your hypothesis 125335633 10/1/2010 26 mathematically and phrase your conclusion precisely.) 125335970 10/1/2010 78 125336423 10/1/2010 41 125339446 10/1/2010 64 125340538 10/1/2010 267 125343444 10/1/2010 16 125356293 10/1/2010 226 125365638 10/1/2010 36 125369580 10/1/2010 46 125370308 10/1/2010 29 125384797 10/1/2010 65 125384981 10/1/2010 94 125391046 10/1/2010 193 125400997 10/1/2010 27 126019495 10/1/2010 94 126019725 10/1/2010 37 126021634 10/1/2010 152 126022692 10/1/2010 149 126029251 10/1/2010 34 126031108 10/1/2010 88 126035487 10/1/2010 82 126039091 10/1/2010 96 126042536 10/1/2010 197 126043327 10/1/2010 202 126047171 10/1/2010 31 126048039 10/1/2010 206 126055040 10/1/2010 166 126058266 10/1/2010 20 126063438 10/1/2010 79 126070772 10/1/2010 140 126072359 10/1/2010 255 126075014 10/1/2010 214 126079142 10/1/2010 43 126079523 10/1/2010 107 126089959 10/1/2010 152 126109278 10/1/2010 124 126124189 10/1/2010 334 126124936 10/1/2010 182 126127258 10/1/2010 287 127023310 10/1/2010 14 127027582 10/1/2010 138 127027819 10/1/2010 85 127031444 10/1/2010 38 127034527 10/1/2010 96 127037084 10/1/2010 155 127045175 10/1/2010 51 127046951 10/1/2010 161 127049464 10/1/2010 355 127056442 10/1/2010 260 127066233 10/1/2010 101 127067302 10/1/2010 273 127067709 10/1/2010 91 127071411 10/1/2010 59 127072160 10/1/2010 60 127076815 10/1/2010 322 127079341 10/1/2010 54 127080741 10/1/2010 132 127081898 10/1/2010 118 127083604 10/1/2010 111 127084357 10/1/2010 188 127085675 10/1/2010 82 127088302 10/1/2010 384 127091788 10/1/2010 90 127093911 10/1/2010 60 127095062 10/1/2010 27 127099273 10/1/2010 101 127105571 10/1/2010 81 128323367 10/1/2010 201 128326577 10/1/2010 112 128328618 10/1/2010 73 128328946 10/1/2010 225 128333478 10/1/2010 23 128336825 10/1/2010 17 128339920 10/1/2010 90 128341159 10/1/2010 283 128342774 10/1/2010 99 128343124 10/1/2010 141 128344122 10/1/2010 166 128346866 10/1/2010 199 128347314 10/1/2010 89 128352984 10/1/2010 53 128356370 10/1/2010 114 128356572 10/1/2010 42 128358051 10/1/2010 224 128362446 10/1/2010 75 128365097 10/1/2010 78 128367558 10/1/2010 277 128369246 10/1/2010 42 128377877 10/1/2010 135 128378385 10/1/2010 251 128378722 10/1/2010 83 128378777 10/1/2010 44 128378898 10/1/2010 71 128379494 10/1/2010 158 128385217 10/1/2010 113 128385944 10/1/2010 39 128392375 10/1/2010 122 128394965 10/1/2010 106 128398149 10/1/2010 33 128399158 10/1/2010 251 128399894 10/1/2010 119 128400616 10/1/2010 163 128403961 10/1/2010 113 128406051 10/1/2010 228 128412722 10/1/2010 63 128413720 10/1/2010 231 128416727 10/1/2010 333 128418119 10/1/2010 70 128418262 10/1/2010 58 128418535 10/1/2010 52 128418694 10/1/2010 211 128419896 10/1/2010 163 128425993 10/1/2010 46 128426714 10/1/2010 201 128428865 10/1/2010 240 128432111 10/1/2010 250 128434678 10/1/2010 163 128435786 10/1/2010 336 128436228 10/1/2010 590 128436501 10/1/2010 27 128438058 10/1/2010 103 128439876 10/1/2010 44 128440144 10/1/2010 170 128441504 10/1/2010 374 128442955 10/1/2010 187 128443111 10/1/2010 67 128446681 10/1/2010 110 128447039 10/1/2010 54 128447877 10/1/2010 323 128453999 10/1/2010 113 128454210 10/1/2010 224 128454310 10/1/2010 9 128456505 10/1/2010 157 128471670 10/1/2010 136 128472996 10/1/2010 418 128475207 10/1/2010 238 128475208 10/1/2010 328 128475246 10/1/2010 19 128475419 10/1/2010 42 128476234 10/1/2010 9 128477495 10/1/2010 384 128481456 10/1/2010 97 128483716 10/1/2010 286 128484348 10/1/2010 45 128486146 10/1/2010 108 128486613 10/1/2010 92 128486630 10/1/2010 13 129174563 10/1/2010 179 129175338 10/1/2010 88 129175535 10/1/2010 197 129177268 10/1/2010 167 129179358 10/1/2010 84 129179714 10/1/2010 181 129182188 10/1/2010 173 129182747 10/1/2010 19 129190345 10/1/2010 75 129190534 10/1/2010 59 129192374 10/1/2010 77 129192410 10/1/2010 70 129195867 10/1/2010 131 129196727 10/1/2010 111 129198659 10/1/2010 90 129199122 10/1/2010 44 129200003 10/1/2010 555 129203156 10/1/2010 277 129203472 10/1/2010 169 129206033 10/1/2010 246 129206861 10/1/2010 167 129208795 10/1/2010 91 129210004 10/1/2010 102 129212701 10/1/2010 81 129213812 10/1/2010 52 129215277 10/1/2010 233 129220332 10/1/2010 163 129222158 10/1/2010 124 129222842 10/1/2010 49 129224281 10/1/2010 109 129225679 10/1/2010 223 129225950 10/1/2010 152 129226725 10/1/2010 35 129227699 10/1/2010 96 129231806 10/1/2010 156 129233328 10/1/2010 76 129236895 10/1/2010 96 129241447 10/1/2010 204 129242271 10/1/2010 144 129246314 10/1/2010 248 129251321 10/1/2010 44 129252929 10/1/2010 319 129253189 10/1/2010 75 129253674 10/1/2010 31 129254417 10/1/2010 16 129256893 10/1/2010 166 129261872 10/1/2010 242 129264631 10/1/2010 80 129267699 10/1/2010 164 129269139 10/1/2010 440 129269235 10/1/2010 296 129270130 10/1/2010 34 129273041 10/1/2010 333 129276237 10/1/2010 147 129282675 10/1/2010 113 129283098 10/1/2010 211 129287376 10/1/2010 61 129290376 10/1/2010 118 129290748 10/1/2010 305 129294700 10/1/2010 64 129297693 10/1/2010 36 129298265 10/1/2010 14 129299403 10/1/2010 62 129300494 10/1/2010 73 129300600 10/1/2010 309 129300710 10/1/2010 206 129304950 10/1/2010 132 129305145 10/1/2010 115 129308103 10/1/2010 123 129308705 10/1/2010 39 129311397 10/1/2010 100 129316198 10/1/2010 210 129316735 10/1/2010 190 129319934 10/1/2010 51 130001647 10/1/2010 318 130003599 10/1/2010 21 130004516 10/1/2010 136 130005887 10/1/2010 115 130008705 10/1/2010 49 130009741 10/1/2010 63 130010822 10/1/2010 66 130011295 10/1/2010 170 130013641 10/1/2010 149 130014615 10/1/2010 320 130015446 10/1/2010 24 130015720 10/1/2010 128 6. (6 pts) A tech service hot line call center is concerned about the duration of inbound calls. You have been tasked with compiling and analyzing the center's call data, below, representing a sample of a day's inbound call volume. (Sec 3.5.6-3.5.7) Customer ID Call date Call duration 125260805 10/1/2010 32 a. Calculate the sample mean and standard deviation for call duration time. 125265384 10/1/2010 163 125266412 10/1/2010 7 125267836 10/1/2010 29 125281795 10/1/2010 84 125282733 10/1/2010 60 125284950 10/1/2010 36 b. Calculate a 95% confidence interval for the mean call duration 125286575 10/1/2010 76 from the sample data. 125292230 10/1/2010 85 125300266 10/1/2010 52 125306688 10/1/2010 39 125311602 10/1/2010 101 125313493 10/1/2010 194 125316250 10/1/2010 283 c. Six months ago, the average call duration was 126. Using your 125320565 10/1/2010 173 confidence interval, test the hypothesis that the current average 125323846 10/1/2010 88 call duration for the entire call center is unchanged from 6 months 125329947 10/1/2010 61 ago, at 95% confidence. (Be sure to state your hypothesis 125335633 10/1/2010 26 mathematically and phrase your conclusion precisely.) 125335970 10/1/2010 78 125336423 10/1/2010 41 125339446 10/1/2010 64 125340538 10/1/2010 267 125343444 10/1/2010 16 125356293 10/1/2010 226 125365638 10/1/2010 36 125369580 10/1/2010 46 125370308 10/1/2010 29 125384797 10/1/2010 65 125384981 10/1/2010 94 125391046 10/1/2010 193 125400997 10/1/2010 27 126019495 10/1/2010 94 126019725 10/1/2010 37 126021634 10/1/2010 152 126022692 10/1/2010 149 126029251 10/1/2010 34 126031108 10/1/2010 88 126035487 10/1/2010 82 126039091 10/1/2010 96 126042536 10/1/2010 197 126043327 10/1/2010 202 126047171 10/1/2010 31 126048039 10/1/2010 206 126055040 10/1/2010 166 126058266 10/1/2010 20 126063438 10/1/2010 79 126070772 10/1/2010 140 126072359 10/1/2010 255 126075014 10/1/2010 214 126079142 10/1/2010 43 126079523 10/1/2010 107 126089959 10/1/2010 152 126109278 10/1/2010 124 126124189 10/1/2010 334 126124936 10/1/2010 182 126127258 10/1/2010 287 127023310 10/1/2010 14 127027582 10/1/2010 138 127027819 10/1/2010 85 127031444 10/1/2010 38 127034527 10/1/2010 96 127037084 10/1/2010 155 127045175 10/1/2010 51 127046951 10/1/2010 161 127049464 10/1/2010 355 127056442 10/1/2010 260 127066233 10/1/2010 101 127067302 10/1/2010 273 127067709 10/1/2010 91 127071411 10/1/2010 59 127072160 10/1/2010 60 127076815 10/1/2010 322 127079341 10/1/2010 54 127080741 10/1/2010 132 127081898 10/1/2010 118 127083604 10/1/2010 111 127084357 10/1/2010 188 127085675 10/1/2010 82 127088302 10/1/2010 384 127091788 10/1/2010 90 127093911 10/1/2010 60 127095062 10/1/2010 27 127099273 10/1/2010 101 127105571 10/1/2010 81 128323367 10/1/2010 201 128326577 10/1/2010 112 128328618 10/1/2010 73 128328946 10/1/2010 225 128333478 10/1/2010 23 128336825 10/1/2010 17 128339920 10/1/2010 90 128341159 10/1/2010 283 128342774 10/1/2010 99 128343124 10/1/2010 141 128344122 10/1/2010 166 128346866 10/1/2010 199 128347314 10/1/2010 89 128352984 10/1/2010 53 128356370 10/1/2010 114 128356572 10/1/2010 42 128358051 10/1/2010 224 128362446 10/1/2010 75 128365097 10/1/2010 78 128367558 10/1/2010 277 128369246 10/1/2010 42 128377877 10/1/2010 135 128378385 10/1/2010 251 128378722 10/1/2010 83 128378777 10/1/2010 44 128378898 10/1/2010 71 128379494 10/1/2010 158 128385217 10/1/2010 113 128385944 10/1/2010 39 128392375 10/1/2010 122 128394965 10/1/2010 106 128398149 10/1/2010 33 128399158 10/1/2010 251 128399894 10/1/2010 119 128400616 10/1/2010 163 128403961 10/1/2010 113 128406051 10/1/2010 228 128412722 10/1/2010 63 128413720 10/1/2010 231 128416727 10/1/2010 333 128418119 10/1/2010 70 128418262 10/1/2010 58 128418535 10/1/2010 52 128418694 10/1/2010 211 128419896 10/1/2010 163 128425993 10/1/2010 46 128426714 10/1/2010 201 128428865 10/1/2010 240 128432111 10/1/2010 250 128434678 10/1/2010 163 128435786 10/1/2010 336 128436228 10/1/2010 590 128436501 10/1/2010 27 128438058 10/1/2010 103 128439876 10/1/2010 44 128440144 10/1/2010 170 128441504 10/1/2010 374 128442955 10/1/2010 187 128443111 10/1/2010 67 128446681 10/1/2010 110 128447039 10/1/2010 54 128447877 10/1/2010 323 128453999 10/1/2010 113 128454210 10/1/2010 224 128454310 10/1/2010 9 128456505 10/1/2010 157 128471670 10/1/2010 136 128472996 10/1/2010 418 128475207 10/1/2010 238 128475208 10/1/2010 328 128475246 10/1/2010 19 128475419 10/1/2010 42 128476234 10/1/2010 9 128477495 10/1/2010 384 128481456 10/1/2010 97 128483716 10/1/2010 286 128484348 10/1/2010 45 128486146 10/1/2010 108 128486613 10/1/2010 92 128486630 10/1/2010 13 129174563 10/1/2010 179 129175338 10/1/2010 88 129175535 10/1/2010 197 129177268 10/1/2010 167 129179358 10/1/2010 84 129179714 10/1/2010 181 129182188 10/1/2010 173 129182747 10/1/2010 19 129190345 10/1/2010 75 129190534 10/1/2010 59 129192374 10/1/2010 77 129192410 10/1/2010 70 129195867 10/1/2010 131 129196727 10/1/2010 111 129198659 10/1/2010 90 129199122 10/1/2010 44 129200003 10/1/2010 555 129203156 10/1/2010 277 129203472 10/1/2010 169 129206033 10/1/2010 246 129206861 10/1/2010 167 129208795 10/1/2010 91 129210004 10/1/2010 102 129212701 10/1/2010 81 129213812 10/1/2010 52 129215277 10/1/2010 233 129220332 10/1/2010 163 129222158 10/1/2010 124 129222842 10/1/2010 49 129224281 10/1/2010 109 129225679 10/1/2010 223 129225950 10/1/2010 152 129226725 10/1/2010 35 129227699 10/1/2010 96 129231806 10/1/2010 156 129233328 10/1/2010 76 129236895 10/1/2010 96 129241447 10/1/2010 204 129242271 10/1/2010 144 129246314 10/1/2010 248 129251321 10/1/2010 44 129252929 10/1/2010 319 129253189 10/1/2010 75 129253674 10/1/2010 31 129254417 10/1/2010 16 129256893 10/1/2010 166 129261872 10/1/2010 242 129264631 10/1/2010 80 129267699 10/1/2010 164 129269139 10/1/2010 440 129269235 10/1/2010 296 129270130 10/1/2010 34 129273041 10/1/2010 333 129276237 10/1/2010 147 129282675 10/1/2010 113 129283098 10/1/2010 211 129287376 10/1/2010 61 129290376 10/1/2010 118 129290748 10/1/2010 305 129294700 10/1/2010 64 129297693 10/1/2010 36 129298265 10/1/2010 14 129299403 10/1/2010 62 129300494 10/1/2010 73 129300600 10/1/2010 309 129300710 10/1/2010 206 129304950 10/1/2010 132 129305145 10/1/2010 115 129308103 10/1/2010 123 129308705 10/1/2010 39 129311397 10/1/2010 100 129316198 10/1/2010 210 129316735 10/1/2010 190 129319934 10/1/2010 51 130001647 10/1/2010 318 130003599 10/1/2010 21 130004516 10/1/2010 136 130005887 10/1/2010 115 130008705 10/1/2010 49 130009741 10/1/2010 63 130010822 10/1/2010 66 130011295 10/1/2010 170 130013641 10/1/2010 149 130014615 10/1/2010 320 130015446 10/1/2010 24 130015720 10/1/2010 128Explanation / Answer
a. Calculate the sample mean and standard deviation for call duration time.
Using technology,
X = sample mean = 135.344 [ANSWER]
s = sample standard deviation = 100.60277 [ANSWER]
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b)
b. Calculate a 95% confidence interval
Note that
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.025
X = sample mean = 135.344
z(alpha/2) = critical z for the confidence interval = 1.959963985
s = sample standard deviation = 100.60277
n = sample size = 250
Thus,
Lower bound = 122.8733806
Upper bound = 147.8146194
Thus, the confidence interval is
( 122.8733806 , 147.8146194 ) [ANSWER]
***********************
c)
As 126 is still inside this confidence interval, then we cannot reject the null hypothesis. There is no significant evidence at 95% confidence that the mean call duration for the entire call center is changed from 6 months ago. [CONCLUSION]
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