Researchers at a food company are interested in how a new spaghetti

Researchers at a food company are interested in how a new spaghetti sauce made from Green tomatoes (and green in color) will compare to their traditional red spaghetti sauce. They are worried that the green color will adversely affect the tastiness scores. They randomly assign subjects to either the green or red sauce condition. Participants indicate the tastiness of the sauce on a 10-point scale. Tastiness scores tend to be skewed. The scores follow:  Red Green  7 4  6 5  9 6  10 8  6 7  7 6  8 9  a) What statistical test should be used to analyze these data? 

As here the sample size is small and the data is not symmetric so we can’t use any parametric test thus we have to use a nonparametric test and in this case the best test would be Wilcoxon rank-sum test for tied case. b) Identify H0 and Ha for this study. 

The null and alternative hypotheses are,

H0: The two samples come from same population i.e. both the samples have same median

Ha: The two samples come from different population i.e. both the samples have different medians c) Conduct the appropriate analysis 

Using Minitab the obtained output is given below,

Mann-Whitney Test and CI: Red, Green

N Median

Red 7 7.000

Green 7 6.000

Point estimate for ETA1-ETA2 is 0.000

95.9 Percent CI for ETA1-ETA2 is (-3.000,2.001)

W = 55.0

Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.7983

The test is significant at 0.7947 (adjusted for ties)

d) Should H0 be rejected? What should the researcher conclude?

As we can see that the p-value for the test is 0.7983 so we are failing to reject the null hypothesis and concluding that the effects of both the sauceis same.

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