Question

1. When it comes to hot dogs, health conscious individuals prefer those that are lowest in salt (sodium) and calories. three types of hot dogs are classified: Beef, poultry, and meat (mix of pork and other types of meats). Additionally, two measure for the hot dogs are provided, one that indicated the number of calories and one that indicated the sodium content.
   1. Run a hypothesis test to determine if there are significant differences in the sodium levels of the three types of hot dogs using an α = 0.05. Describe the differences if differences exist.
   2. Run a hypothesis test to determine if there are significant differences in the calorie content of the three types of hot dogs using α = 0.05. Describe the differences if differences exist.

Type Calories Sodium

1   181   477
1   176   425
1   149   322
1   184   482
1   190   587
1   158   370
1   139   322
1   175   479
1   148   375
1   152   330
1   111   300
1   141   386
1   153   401
1   190   645
1   157   440
1   131   317
1   149   319
1   135   298
1   132   253
2   173   458
2   191   506
2   182   473
2   190   545
2   172   496
2   147   360
2   146   387
2   139   386
2   175   507
2   136   393
2   179   405
2   153   372
2   107   144
2   195   511
2   135   405
2   140   428
2   138   339
3   129   430
3   132   375
3   102   396
3   106   383
3   94   387
3   102   542
3   87   359
3   99   357
3   107   528
3   113   513
3   135   426
3   142   513
3   86   358
3   143   581
3   152   588
3   146   522
3   144   545

Answer 1

For sodium:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Type 1	19	7528	396.2105263	10560.73099
Type 2	17	7115	418.5294118	8812.014706
Type 3	17	7803	459	7180.75
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	35993.85	2	17996.92605	2.017694879	0.143646	3.18261
Within Groups	445977.4	50	8919.547864
Total	481971.2	52

The p-value is 0.1436

Since p-value is greater than 0.05 so we cannot conclude that there are significant differences in the sodium levels of the three types of hot dogs using an α = 0.05.

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For calories:

One factor ANOVA Mean 155.3 158.7 118.8 144.7 n Std. Dev 19 17 25.24 Type 2 17 53 22.17 Type 1 22.55 Type 3 29.12 Total ANOVA table Source df MS F p-value 15.56 5.58E-06 Treatment1 Error Total 6,910.85 27,172.69 44,083.55 2 8,455.427 50 543.454 52 Post hoc analysis p-values for pairwise t-tests Type 3 118.8 Type 1 155.3 Type 2 158.7 Type 3118.8 Type 1 155.3 2.10E-05 Type 2 158.7 7.56E-06 6650 Tukey simultaneous comparison t-values (d.f. - 50) Type 3 118.8 Type 1 155.3 Type 2 158.7 Type 3118.8 Type 1 Type 2 158.7 155.3 4.70 5.00 0.44 critical values for experimentwise error rate 0.05 0.01 2.42 3.06

The p-value is: 0.0000

Since p-value is less than 0.05 so we can conclude that there are significant differences in the calorie content of the three types of hot dogs using α = 0.05.

Difference exist between Type 1 - Type 3 and Type 2 - Type 3