Comparing the life expectancy in `C` and` D` batteries in toys vs. electronics

Comparing the life expectancy in `C` and` D` batteries in toys vs - Comparing the life expectancy in `C` and` D` batteries in toys vs. electronics introduction. electronics

Batteries type C and D have often been compared in quality in terms of lifetime. Both batteries are extensively used in recreational devices for children (toys) as well as simple household devices (electronics). This paper’s objective was to determine whether the categorical factors of battery type and usage significantly affect the quantitative variable of battery lifetime. Similar studies suggest that this experiment can be carried out by first using a two-way ANOVA to determine if there are any effects at all coming from the two categorical factors mentioned and their interaction, and then conducting multiple paired t-tests in order to determine significance of the differences (Oswald 126). A sample of 43 battery operated toys and 43 battery operated electronics was selected for the experiment. Each sample was powered first by battery C and then by battery D after the first battery had run out. The process was reversed for the next sample which was powered first by battery D and then by battery C. This was done to deny the presence of any bias in the experiment with respect to precedence. This procedure was conducted both for the toys and the electronics. The data analysis feature of Microsoft Excel which was used extensively in this paper offers an excellent utility for calculating the necessary descriptive and inferential statistics and for creating charts to facilitate better explanation of results. (Simon 48).

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Table 1 presents raw data to be used as the sample for this experiment. Chart 1 and 2 shows that in either case of usage (toys and electronics respectively), battery C generally provide higher life expectancies than D.

            The descriptive data in table 2 indicates a fairly normal distribution with mean and standard deviation of lifetime for battery C 651.49±157.35 for toys and 638.70±180.19. Battery D had 460.86±143.19 for toys and 452.47±174.13. Table 2 also supports charts 1 and 2 on the general superiority of battery C as compared to battery D. Average lifetime for both batteries were noted to be higher in toys than in electronics.

The first hypothesis tested was is there no significant difference in the lifetime expectancy of batteries between types C and D and between usages Toys and Electronics. Summary of the two-way ANOVA conducted for this hypothesis at a 95% confidence level (see table 3) shows that the obtained F-value for both usage and interaction (0.18 and 0.01 respectively), is lower than the critical F-value of 3.897 which means that there is no significant difference in lifetime expectancy of batteries used for toys and those used for electronics. Other the other hand, obtained F-value of 56.52 for battery type is greater than the same critical value which indicates that there is a significant difference in lifetime expectancy of battery type C and D.

Since the presence of difference was not established for usage, there was no more need to follow up with paired t-tests for usage. To establish the significance of the difference of life expectancy of battery type C from D, a paired t-test was conducted separately for toys and for electronics. The results for the paired t-test between batteries C and D used for toys are summarized in table 4. The obtained t-value of 5.95 is greater than the critical value of 2.018 at a 95% confidence level. This means that battery type C has a significantly higher life expectancy than battery type D when used for toys.

Table 5 showed similar outcome from electronics usage. The obtained t-value of 4.74 is also greater than the critical value 2.018 at a 95% confidence level. This means that battery type C also performs better than type D in terms of life expectancy in electronics.

Conclusion

            It was established by the results from the statistical inferences made by this paper that usage between toys and electronics is not a significant factor when determining life expectancy in batteries type C and D. Furthermore, this paper supports the claim that battery C performs better than battery D in terms of life expectancy in usage both for toys and electronics.

Tables

Table 1: Raw data on battery lifetime (in minutes)
Usage: Toys
Battery type

Usage: Electronics
Battery type
Sample
C
D

Sample
C
D
Toy 1
752
465

Electronics 1
744
496
Toy 2
498
433

Electronics 2
420
523
Toy 3
805
652

Electronics 3
599
279
Toy 4
485
499

Electronics 4
926
530
Toy 5
741
608

Electronics 5
582
757
Toy 6
844
310

Electronics 6
371
426
Toy 7
626
541

Electronics 7
863
254
Toy 8
741
457

Electronics 8
524
686
Toy 9
658
613

Electronics 9
903
234
Toy 10
656
298

Electronics 10
575
448
Toy 11
561
229

Electronics 11
549
668
Toy 12
696
413

Electronics 12
658
623
Toy 13
735
677

Electronics 13
421
534
Toy 14
773
484

Electronics 14
861
330
Toy 15
412
302

Electronics 15
617
716
Toy 16
684
269

Electronics 16
736
387
Toy 17
488
367

Electronics 17
493
223
Toy 18
470
541

Electronics 18
617
509
Toy 19
511
567

Electronics 19
379
786
Toy 20
467
486

Electronics 20
391
269
Toy 21
914
303

Electronics 21
746
287
Toy 22
369
426

Electronics 22
367
443
Toy 23
467
454

Electronics 23
396
425
Toy 24
756
267

Electronics 24
683
607
Toy 25
505
550

Electronics 25
740
374
Toy 26
586
202

Electronics 26
449
281
Toy 27
671
504

Electronics 27
894
217
Toy 28
409
566

Electronics 28
698
676
Toy 29
783
423

Electronics 29
416
497
Toy 30
899
695

Electronics 30
549
306
Toy 31
739
587

Electronics 31
485
276
Toy 32
751
458

Electronics 32
948
683
Toy 33
949
422

Electronics 33
440
247
Toy 34
552
419

Electronics 34
576
465
Toy 35
721
757

Electronics 35
700
394
Toy 36
806
546

Electronics 36
808
546
Toy 37
920
612

Electronics 37
557
621
Toy 38
509
434

Electronics 38
698
209
Toy 39
829
229

Electronics 39
948
250
Toy 40
609
253

Electronics 40
778
587
Toy 41
666
337

Electronics 41
659
210
Toy 42
610
435

Electronics 42
767
475
Toy 43
391
727

Electronics 43
933
702

Table 2: Descriptive data of sample

Usage: Toys

Usage: Electronics

C
D

C
D
Mean
651.4884
460.8605

Mean
638.6976744
452.4651
Standard Error
23.99521
21.83657

Standard Error
27.47810031
26.55395
Median
666
457

Median
617
448
Mode
741
541

Mode
549
#N/A
Standard Deviation
157.3471
143.1919

Standard Deviation
180.1859535
174.1259
Sample Variance
24758.11
20503.93

Sample Variance
32466.97785
30319.83
Kurtosis
-0.95315
-0.66722

Kurtosis
-1.082264614
-1.1841
Skewness
-0.00629
0.062574

Skewness
0.157123111
0.20002
Range
580
555

Range
581
577
Minimum
369
202

Minimum
367
209
Maximum
949
757

Maximum
948
786
Sum
28014
19817

Sum
27464
19456
Count
43
43

Count
43
43

Table 3: 2-way ANOVA

Source of Variation
SS
df
MS
F
P-value
F crit
Sample
4825.122
1
4825.122
0.178627
0.673096
3.897407
Columns
1526756
1
1526756
56.52095
3.17E-12
3.897407
Interaction
207.6802
1
207.6802
0.007688
0.930233
3.897407
Within
4538052
168
27012.21

Total
6069840
171

Table 4:

Table 5:

t-Test: Paired Two Sample for Means

t-Test: Paired Two Sample for Means

C
D

C
D
Mean
651.4884
460.8605
Mean
638.6977
452.4651
Variance
24758.11
20503.93
Variance
32466.98
30319.83
Observations
43
43
Observations
43
43
Pearson Correlation
0.024526

Pearson Correlation
-0.05569

Hypothesized Mean Difference
0

Hypothesized Mean Difference
0

Df
42

df
42

t Stat
5.948694

t Stat
4.743446

P(T<=t) two-tail
4.71E-07

P(T<=t) two-tail
2.44E-05

t Critical two-tail
2.018082

t Critical two-tail
2.018082

Charts

Chart 1

Chart 2

References:

Oswald, Richard. “An experimental comparison of bio-cell batteries to other conventional types.” Australian Journal of Engineering (2001): 125 – 132

Simon, Jinger. Excel 2000 in a Nutshell: A Power User’s Quick Reference. O’Reilly: 2000

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