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. Assume equal population variances. The mean difference in ratings was d¯d¯ = -0.38571 with a standard deviation of s_d = 1.37570. Use α = 0.05.

 

(a) Choose the appropriate hypotheses for a two-tailed test. Assume μ_d is the average difference in the taste of the two sauces.

 

multiple choice 1

• H₀: μ_d ≤ 0 versus H₁: μ_d > 0

• H₀: μ_d = 0 versus H₁: μ_d ≠ 0

• H₀: μ_d ≥ 0 versus H₁: μ_d < 0

 

(b) Find the test statistic t_calc. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)

 

t_calc         

 

(c) Find the critical value t_crit for α = .05. (Round your answer to 3 decimal places.)

 

t_crit         +/-

 

(d) Find the p-value. (Round your answer to 3 decimal places.)

 

p-value          

 

(e) State your conclusion.

 

We   (Click to select)   can   cannot  conclude that there is a difference in the taste of the two sauces.