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, 70 tasters were asked to rate their satisfaction with two different sauces on a scale of 1–10, with 10 being the highest. The mean difference in ratings was d¯d¯ = –0.385714 with a standard deviation of sd = 1.37570. Use α = .05. (a) Choose the appropriate hypotheses for a two-tailed test. Assume μd is the average difference in taste of the two sauces. H0: μd = 0 versus H1: μd ≠ 0 H0:μd ≥ 0 versus H1: μd < 0 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 4 decimal places.) p-value
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, 70 tasters were asked to rate their satisfaction with two different sauces on a scale of 1–10, with 10 being the highest. The mean difference in ratings was d¯d¯ = –0.385714 with a standard deviation of sd = 1.37570. Use α = .05.
(a) Choose the appropriate hypotheses for a two-tailed test. Assume μd is the average difference in taste of the two sauces.
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H0: μd = 0 versus H1: μd ≠ 0
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H0:μd ≥ 0 versus H1: μd < 0
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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 4 decimal places.)
p-value
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