ANOVA Analysis :

  1. Piglets were assigned randomly to each of four groups. Each group was given a different kind of feed. Below are the weights of the piglets after one year on these special diets. What, if anything, can you concluude?


  2. Ans:

    1)
    We have feed1 of three groups, we will check if the different kind of feed given to three groups showed significant difference in weights or not.
    To do that we will do ANOVA analysis.

    Null Hypothesis:There is no difference in the groups mean of three different groups of feed1.

    Alternative Hypothesis:There is significant difference in the groups mean of three different groups of feed1.

    SUMMARY

    Groups Count Sum Average Variance
    Feed1_gr1  5 666.8 133.36 46.348
    Feed1_gr2  5 762.2 152.44 40.963
    Feed1_gr3  4 883.1 220.775 37.2825

    ANOVA


    Conclusion :We can see from the above table that p-value is 0.00, hence we can reject null hypothesis and conclue that their is a significant difference in the means of three groups. In other words, the different feed given to different groups did affect significantly.


  3. The amount of food consumed by adult deer during 4 months was recorded. Is there evidence to show that deer feeding habits change during the year ?



  4. Ans:

    2)
    We will to ANOVA analysis to check that.
    Null Hypothesis:There is no evidence that deer feeding habits changed during the year.

    Null Hypothesis:There is evidence that deer feeding habits changed during the year.

    SUMMARY

    Groups Count Sum Average Variance
    Feb  5 24.1 4.82 0.017
    May  6 26 4.333333 0.030667
    Aug  6 28 4.666667 0.022667
    Nov  5 26.2 5.24 0.073

    ANOVA


    Conclusion :Since the p-value in the above table is 0.00, Hence we reject the null hypothesis and conclude that their is a evidence that deer feeding habbits changed during the year.

  5. Do good smells bring good business?Businesses know that customers often respond to background music. Do they also respond to odors? Nicolas Gueguen and his colleagues studied this question in a small pizza restaurant in France on Saturday evenings in May. On one evening, a relaxing lavender odor was spread the restaurant; on another evening, a stimulating lemon odor; a third evening served as a control, with no odor. The three evenings were comparable in many ways (weather, customer count, and so on), so we are willing to regard the data as independent SRSs from spring Saturday evenings at this restaurant. Table contains data on how long (in minutes) customers stayed in the restaurant on each of the three evenings.

    • (a) Make an appropriate graph comparing the customer times for each evening. Do any of the distributions show outliers, strong skewness, of other clear deviations from Normality?
    • (b) Do a compete analysis to see whether the groups differ in the average amount of time spent in the restaurant. Follow the four-step precess in your work. Did you find anythig surprising?



    Ans:

    a)


             

    1) We can clearly interpret from the above boxplot that

    • a) Lavender has an outlier and also
    • b) it is skewed. It is left skewed
    • c) Since it is skewed hence not normal

    Lemon and no order have symmetric distribution.


    b)

    We will do ANOVA anaylsis to check the group diifer or not.

    Steps1
      Null hypothesis:The mean of the three group are same.
      Alternative hypothesis: The mean of the any two groups are significantly different.

    Steps2
      Confidence interval = 95%

    Steps3: Test Statistic

    SUMMARY

    Groups Count Sum Average Variance
    Lavender Odor  30 3171 105.70 171.73
    lemon Odor  28 2514 89.79 238.32
    No odor  30 2738 491.27 222.89

    ANOVA

    Source of Variation  SS df  MS  F P-value  F crit
    Between Groups 4569.02 2.00 2284.51 10.86  0.00  3.10
    Within Groups 17878.88 85.00 210.34
    Total 22447.987

    Conclusion: From the above table we can see the p-value is 0.00 which is less than 0.05. Hence we reject null hypothesis and conclude that the mean of the any two groups are significantly different.