In 2009 Noodles & Company introduced spaghetti and meatballs to its menu. Before putting it on the menu, it performed taste tests to determine the best-tasting spaghetti sauce. In a paired comparison, 42 tasters were asked to rate their satisfaction with two different sauces on a scale of 1–10, with 10 being the highest. Assume equal population variances. The mean difference in ratings was d⎯⎯d¯ = -0.37223 with a standard deviation of sd = 1.75260. Use α = 0.05. (a) Choose the appropriate hypotheses for a two-tailed test. Assume μd is the average difference in the taste of the two sauces. multiple choice H0: μd ≥ 0 versus H1: μd < 0 H0: μd = 0 versus H1: μd ≠ 0 Correct H0: μd ≤ 0 versus H1: μd > 0 (b) Find the test statistic tcalc. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.) tcalc (c) Find the critical value tcrit for α = .05. (Round your answer to 3 decimal places.) tcrit +/- (d) Find the p-value. (Round your answer to 3 decimal places.) p-value (e) State your conclusion. We cannot Correctconclude that there is a difference in the taste of the two sauces.
In 2009 Noodles & Company introduced spaghetti and meatballs to its menu. Before putting it on the menu, it performed taste tests to determine the best-tasting spaghetti sauce. In a paired comparison, 42 tasters were asked to rate their satisfaction with two different sauces on a scale of 1–10, with 10 being the highest. Assume equal population variances. The mean difference in ratings was d⎯⎯d¯ = -0.37223 with a standard deviation of sd = 1.75260. Use α = 0.05.
(a) Choose the appropriate hypotheses for a two-tailed test. Assume μd is the average difference in the taste of the two sauces.
multiple choice
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H0: μd ≥ 0 versus H1: μd < 0
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H0: μd = 0 versus H1: μd ≠ 0 Correct
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H0: μd ≤ 0 versus H1: μd > 0
(b) Find the test statistic tcalc. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)
tcalc
(c) Find the critical value tcrit for α = .05. (Round your answer to 3 decimal places.)
tcrit +/-
(d) Find the p-value. (Round your answer to 3 decimal places.)
p-value
(e) State your conclusion.
We cannot Correctconclude that there is a difference in the taste of the two sauces.
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