Question

A university student decided to set up a formal experiment to see if ants are more attracted to some common sandwich fillings. He chose three types of fillings to compare: vegemite, peanut butter, and ham & pickles. After several minutes he placed a jar over the sandwich bit and counted the number of ants. He repeated this process eight times to get eight samples. The data are stored in the file SandwichAnts.

a. State hypotheses.

b. Open the data set in Descriptive Statistics to generate comparative boxplots and summary statistics. Include a screenshot of this page with your submission. Check conditions for using the Fdistribution. Explain how each condition is verified, violated, or not possible to verify.

c. Open the data set in ANOVA for Difference in Means. Include a screen shot of the information under “Original Sample”. Fill in the blanks below, and shade in the appropriate tail area in the F distribution curve and use it to estimate the p-value.

F =

Degrees of freedom for groups =

Degrees of freedom for error =

p-value estimate =

Conclusion for Overall test =

d. If you reject Ho, construct a confidence interval for the mean for each group, using the MSE. Which sandwich fillings (if any) are different? Which filling(s) did the ants like he most? Which did they like the least?

Butter  Filling Bread   Ants    Order
no      Vegemite        Rye     18      10
no      Peanut Butter   Rye     43      26
no      Ham & Pickles       Rye     44      39
no      Vegemite        Wholemeal       29      25
no      Peanut Butter   Wholemeal       59      35
no      Ham & Pickles       Wholemeal       34      1
no      Vegemite        Multigrain      42      44
no      Peanut Butter   Multigrain      22      36
no      Ham & Pickles       Multigrain      36      32
no      Vegemite        White   42      33
no      Peanut Butter   White   25      34
no      Ham & Pickles       White   49      13
no      Vegemite        Rye     31      14
no      Peanut Butter   Rye     36      31
no      Ham & Pickles       Rye     54      20
no      Vegemite        Wholemeal       21      19
no      Peanut Butter   Wholemeal       47      38
no      Ham & Pickles       Wholemeal       65      5
no      Vegemite        Multigrain      38      21
no      Peanut Butter   Multigrain      19      22
no      Ham & Pickles       Multigrain      59      8
no      Vegemite        White   25      41
no      Peanut Butter   White   21      16
no      Ham & Pickles       White   53      23

Butter	Filling	Bread	Ants	Order
no	Vegemite	Rye	18	10
no	Peanut Butter	Rye	43	26
no	Ham & Pickles	Rye	44	39
no	Vegemite	Wholemeal	29	25
no	Peanut Butter	Wholemeal	59	35
no	Ham & Pickles	Wholemeal	34	1
no	Vegemite	Multigrain	42	44
no	Peanut Butter	Multigrain	22	36
no	Ham & Pickles	Multigrain	36	32
no	Vegemite	White	42	33
no	Peanut Butter	White	25	34
no	Ham & Pickles	White	49	13
no	Vegemite	Rye	31	14
no	Peanut Butter	Rye	36	31
no	Ham & Pickles	Rye	54	20
no	Vegemite	Wholemeal	21	19
no	Peanut Butter	Wholemeal	47	38
no	Ham & Pickles	Wholemeal	65	5
no	Vegemite	Multigrain	38	21
no	Peanut Butter	Multigrain	19	22
no	Ham & Pickles	Multigrain	59	8
no	Vegemite	White	25	41
no	Peanut Butter	White	21	16
no	Ham & Pickles	White	53	23

Answer 1

a. State hypotheses.

Ans: Null Hypothesis: The mean number of at to three types of filling are same

Alternative Hypothesis: At least one type of filling has a significant difference mean number of ant.

b)

ByVar1	Mean1	StDev1	Minimum1	Maximum1	N1
Ham & Pickles	49.25	10.79352	34	65	8
Peanut Butter	34	14.62874	19	59	8
Vegemite	30.75	9.254343	18	42	8

From the summary of the data and box plot, we know that the filling types Ham & Pickles and Vegemite may have a significant mean number of ants.

c)

One-way ANOVA: Ants versus Filling

Source	DF	SS	MS	F	P
Filling	2	1561	781	5.63	0.011
Error	21	2913	139
Total	23	4474

S = 11.78 R-Sq = 34.89% R-Sq(adj) = 28.69%

Degrees of freedom for groups = 2

Degrees of freedom for error = 21

p-value estimate = 0.011

Conclusion for Overall test: We reject the null hypothesis and conclude that there is at least one type of filling has a significant mean number of ants from the other remaining types of filling at 0.05 level of significance.

d. If you reject Ho, construct a confidence interval for the mean for each group, using the MSE. Which sandwich fillings (if any) are different? Which filling(s) did the ants like the most? Which did they like the least?\

Ans:

The sandwich fillings Ham & Pickles and Peanut Butter, and Ham & Pickles and Vegemite are different. Ham & Pickles filling did the ants like the most. Vegemite did they like the least.