A chef in a restaurant that specializes in pasta dishes was experiencing difficu
ID: 3299555 • Letter: A
Question
A chef in a restaurant that specializes in pasta dishes was experiencing difficulty in getting brands of pasta to be al dente – that is, cooked enough so as to not feel starchy or hard but still feel firm when bitten into. The chef decided to conduct an experiment in which two brands of pasta, one American and one Italian, were cooked for either 4 or 8 minutes. The variable of interest was weight of the pasta because cooking the pasta enables it to absorb water. Pasta with a faster rate of water absorption may provide a shorter interval in which the pasta is al dente, thereby increasing the chance that it might be overcooked. The experiment was conducted by using 150 grams of uncooked pasta. Each trial began by bringing a pot containing 6 quarts of cold, unsalted water to a moderate boil. The 150 grams of uncooked pasta was added and then weighed after a given period of time by lifting the pasta from the pot via a built-instrainer. The results (weight in grams) for two replicates of each type of pasta and cooking time are provided for you in Pasta.xls.
At the 0.05 level of significance, þ
1. Is there an interaction between type of pasta and cooking time? a. State the decision rule b. Report the test statistic c. Report the results/findings of your statistical analysis
2. Is there an effect due to type of pasta? a. State the decision rule b. Report the test statistic c. Report the results/findings of your statistical analysis
3. Is there an effect due to cooking time? a. State the decision rule b. Report the test statistic c. Report the results/findings of your statistical analysis
Type Four Eight A 265 310 A 270 320 I 250 300 I 245 305Explanation / Answer
Q1.
Given table data is as below
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calculation formula for E table matrix
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expected frequecies calculated by applying E - table matrix formulae
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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above
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set up null vs alternative as
null, Ho: no relation b/w X and Y OR X and Y are independent / interaction between type of pasta and cooking time
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
level of significance, = 0.05
from standard normal table, chi square value at right tailed, ^2 /2 =7.815
since our test is right tailed,reject Ho when ^2 o > 7.815
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 0.298
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 4 - 1 ) = 1 * 3 = 3 is 7.815
we got | ^2| = 0.298 & | ^2 | =7.815
make decision
hence value of | ^2 o | < | ^2 | and here we do not reject Ho
ANSWERS
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null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
test statistic: 0.298
critical value: 7.815
decision: do not reject Ho
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