Question

3.10 Corny Flavors 5 pts. Suppose you work for the Frito-Day serpecation in their new foods development division. They have developed a new additive they've called Veriixesh. They want to add this additive to for their corn tortilla chips because it makes them stay crisp up to three times longer. However, the preservative also adds a taste which might be unpleasant. You are asked to test whether or not Kerifxesh. is perceived by people as unpleasent, You divide 90 test subjects into three randomly assigned groups (30 people in each group). Group 1 tastes the chips made without VexiFresh and group 2 tastes them made with a small amount of Kexitxesk and group 3 tastes them with a large amount of Verifireshe. The study participants report how well they like the chips on a scale of 1 to 5, with 5 being best. [Think of these rankings as Bad, OK, GOOD etc.] What statistic can you use to determine whether or not KexiExesh effects taste appeal in the tortilla chips? What would you conclude if you computed a value of -2.5 for this statistic A. Name the appropriate statistical analysis B. Report the result in proper (APA) statistical reporting format. C. Interpretation 3.11 A Harvest of Pearls 5 pts. You are a partner in a start-up aquaculture company that raises oysters to produce cultured pearls. Your technician comes to you with the results of the latest test of pearl yields from two beds of oysters raised under identical conditions except for the pearl stimulant. One bed was treated with the traditional grains-of-sand and the other with a synthetic pure-silicon pearl induction treatment. Your technician provides you with the sizes of the 100 pearls that have been harvested (50 from each bed) and she tells you that both samples appear to be bi-modally distributed. What statistic would you use to see if the pearl stimulant has an effect on the size of the pearls produced? What would it mean if you calculated a value of -1.00 for this statistic? A. Name the appropriate statistical analysis B. Report the result in proper (APA) statistical reporting format. C. Interpretation

Answer 1

An One factor ANOVA is the most suitable analysis for the above problem. ie to compare three or more groups.

The null hypothesis is that verifresh has not affected the taste appeal in tortilla chips vs the alternative that verifresh affect the taste appeal in tortilla chips.

The degrees of freedom are (no: of groups-1)=3-1=2; and ( total observation -no:of groups)=90-3=87

The critical value is for (2,87) degrees of freedom is 3.11 from the F table for 0.05 significance level or alpha. The statistic should follow F distribution which takes values from 0 to infinity. so we call the statistic, F statistic, which is the ratio of two variances , that cannot be negative. so the F statistic will always take value >0. So I take the magnitude of the statistic value ie 2.5. Since 2.5 < critical value(3.11) we cannot reject the null hypothesis at 5% alpha that the verifresh has not affected the taste appeal in tortilla chips.

A two sample t test would be appropriate in this case here we test whether pearl stimulant has an effect on the size of pearl produced which is considered to be our alternative hypothesis. where the null hypothesis is pearl stimulant has no effect on the size of pearl produced. The test is one tailed as we are interested in knowing our treatment is effective.

The value of t statistic is 1 and the critical value for 98 degrees of freedom and 5% alpha is 1.661

SurfStat t-distribution calculator -t 0t t 0 vil probability d.f. t value 0.05 1.661 98

Since t statistic <1.661 we cannot reject the null hypothesis. Hence we conclude that the treatment is not effective.