Frito-Lay, Inc. now manufactures Cheetos Crunchy brands in several flavors. We h

Question

Frito-Lay, Inc. now manufactures Cheetos Crunchy brands in several flavors. We have introduced a study of snack length using regular original flavor snacks in small 1 oz. servings classifying the snacks into "r", "s", "l" lengths in addition to actual length in mm. An additional flavor, "flamin hot" available also in 1 oz. servings has also been selected. Two bags of each flavor have been measured and classified.

answer the following questions:

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 obtained from the parametric tests on the means of each group. List them. Are they different intervals and do they overlap?

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

E) Are the distributions in the two groups the same? are the data in the two groups approximately normally distributed?

two flavors data

Bag Type Lengthmm 1 l 59.5 1 l 70.5 1 l 54.5 1 l 54 1 l 62.5 1 s 31.5 1 l 53.5 1 s 30 1 s 21 1 l 46.5 1 r 10 1 r 11 1 r 10 1 r 12 1 r 8 1 s 29 1 l 57.5 1 l 53 1 l 58 1 l 65.5 1 l 54 1 s 32 1 l 50 1 l 68 1 r 6.5 1 l 55 1 s 37 1 s 32 1 s 24.5 1 r 11 1 s 37 1 s 27.5 1 s 26 1 s 33 1 l 63.5 1 s 20 1 r 12 1 s 18 1 r 10 1 s 37 1 r 11 1 r 6 2 l 63 2 s 36.5 2 l 47 2 l 48 2 l 49 2 l 45.5 2 s 23.5 2 s 34.5 2 s 36 2 l 44.5 2 l 45 2 l 44 2 s 22 2 s 34 2 l 49 2 l 46.5 2 l 46.5 2 r 15 2 s 19 2 s 24.5 2 l 62 2 l 56 2 s 26.5 2 l 47 2 l 41.5 2 s 23.5 2 s 27.5 2 s 29 2 s 31 2 l 48.5 2 l 53 2 l 51.5 2 l 42 2 l 42.5 2 r 6 2 r 4

Explanation / Answer

a) using F test and excel for analysis.

Since F falls in the acceptance region, we accept the null hypothesis.

Since p value is > 0.05, we accept the null hypothesis.

B) The variances are equal.

C) For the first sample

For the second sampel

The two intervals overlap.

D)

n=(*(z1+z1)/0)^2

using this formula, we get n=464

E) Here we use goodness of fit test to confirm the distirbuion. since the sample size is large(>30), both the amples ae approximately normal. we can confirm this by goodness of fit.

For the first sample,

p value is > 0.05, so normal distirbuton is a goodfit.

Since p value is < 0.05, the normal distirbuion is not a good fit.

F-Test Two-Sample for Variances Variable 1 Variable 2 Mean 34.96428571 37.90277778 Variance 417.4925958 207.3831349 Observations 42 36 df 41 35 F 2.013146324 P(F<=f) one-tail 0.018421585 F Critical one-tail 1.731296767

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