Question

Frito-Lay, Inc. now manufactures Cheetos Crunchy brand snacks in several flavors. We have measured the snacks by snack length in mm using regular original flavor snacks in small 1oz servings. An additional flavor, "Flaming Hot", available also in 1 oz servings has also been selected. Two bags of each flavor have been measured and classified. The two bags of each flavor have been measured and classified. The two bags are necessary to achieve a suitable total number and have been verified as not being of different length.

A. Are the lengths different for the two groups? Use two different tests, at least one of which is nonparametric.

B. Are the variances the same?

C. Compare the 95% confidence intervals for the means of each flavor obtained from the parametric tests on data. Are they different intervals?

D. If we wanted to confirm these results with a balanced trial (= sample size) and the difference of the means observed to two places as the difference to be observed using a variance of 300, how many samples would we need in each flavor if we wanted a power of 0.8?

E. Are the data in the two groups approximately normally distributed?

MAKE SURE ITS R VS. F AND NOT COMPARING BAGS. Give hypotheses, significance levels, tests performed, statistics, and conclusions.

Flavor	Bag	Type	Length (mm)
r	1	l	59.5
r	1	l	70.5
r	1	l	54.5
r	1	l	54
r	1	l	62.5
r	1	s	31.5
r	1	l	53.5
r	1	s	30
r	1	s	21
r	1	l	46.5
r	1	r	10
r	1	r	11
r	1	r	10
r	1	r	12
r	1	r	8
r	1	s	29
r	1	l	57.5
r	1	l	53
r	1	l	58
r	1	l	65.5
r	1	l	54
r	1	s	32
r	1	l	50
r	1	l	68
r	1	r	6.5
r	1	l	55
r	1	s	37
r	1	s	32
r	1	s	24.5
r	1	r	11
r	1	s	37
r	1	s	27.5
r	1	s	26
r	1	s	33
r	1	l	63.5
r	1	s	20
r	1	r	12
r	1	s	18
r	1	r	10
r	1	s	37
r	1	r	11
r	1	r	6
r	2	l	63
r	2	s	36.5
r	2	l	47
r	2	l	48
r	2	l	49
r	2	l	45.5
r	2	s	23.5
r	2	s	34.5
r	2	s	36
r	2	l	44.5
r	2	l	45
r	2	l	44
r	2	s	22
r	2	s	34
r	2	l	49
r	2	l	46.5
r	2	l	46.5
r	2	r	15
r	2	s	19
r	2	s	24.5
r	2	l	62
r	2	l	56
r	2	s	26.5
r	2	l	47
r	2	l	41.5
r	2	s	23.5
r	2	s	27.5
r	2	s	29
r	2	s	31
r	2	l	48.5
r	2	l	53
r	2	l	51.5
r	2	l	42
r	2	l	42.5
r	2	r	6
r	2	r	4
f	1	l	42
f	1	s	38.5
f	1	l	40.5
f	1	l	48.5
f	1	l	64.1
f	1	l	64
f	1	s	33
f	1	l	64.2
f	1	s	38
f	1	l	41.1
f	1	l	49.9
f	1	l	62.6
f	1	r	11.4
f	1	l	61.1
f	1	s	35
f	1	l	62.2
f	1	l	46.5
f	1	s	19.5
f	1	r	15.1
f	1	s	32.2
f	1	l	50
f	1	s	18.9
f	1	s	29
f	1	l	52.2
f	1	l	59.8
f	1	s	36.5
f	1	l	55
f	1	r	12.2
f	1	r	10
f	1	r	5.5
f	2	l	62
f	2	s	39
f	2	l	48
f	2	l	62
f	2	s	28.3
f	2	l	68
f	2	l	60
f	2	l	50.2
f	2	s	38.2
f	2	l	56.4
f	2	l	41.8
f	2	r	9.8
f	2	s	30
f	2	l	51.4
f	2	l	52
f	2	l	40.4
f	2	l	60.5
f	2	l	52.8
f	2	l	53.2
f	2	s	26.6
f	2	l	61
f	2	s	37.1
f	2	s	28
f	2	l	62.5
f	2	s	39.9
f	2	l	62.2
f	2	s	39

Answer 1

Using Minitab:

A:

First Use Non-Parametric Test: Mann Whitney u test for two sample.

Hypothesis:

H0 : Median(r) = Median(f)

H1 : Median(r) not equal Median(f)

alpha = 0.05

p-value = 0.0243 is less than 0.05, reject the null hypothesis, there is a significant difference in median of length of flavor.

Second, Use Parametric Test: Two sample T-test.

Hypothesis:

H0: mean(r) = mean(f)

H1: mean(r) not equal mean(f)

alpha = 0.05

p-value = 0.025 is less than 0.05,reject the null hypothesis, there is a significant difference between the mean of length of flavor.

B:

Use Levene test to check variance are equal or not:

Use Levene test when we dont know distribution of the data.

H0: variance are equal

H1: variance are not equal

alpha = 0.05

p-value = 0.403 is greater than 0.05, do not reject the null hypothesis, so variance are equal.

(C): Yes, Parametric and Non-Parametric test give different 95% confidence interval.

You can see from above result of Parametric and Non-Parametric test.

(D): 107 samples would we need in each flavor if we wanted a power of 0.8.

(E):

H0: data is normal

H1: data not normal

alpha = 0.05

p-value is <0.005 is less than 0.05, reject the null hypothesis, data not normal.

So data is not normal we need to use non-parametric test.