Question

In 2009 Noodles & Company introduced spaghetti and meatballs to their menu. Before putting it on the menu, they 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=–0.385714 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 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. A negative value should be indicated by a minus sign.)

  

tcrit__________

+/-

(d)	Find the p-value. (Round your answer to 4 decimal places.)

p-value________

(e)	State your conclusion.

We (can/cannot)

conclude that there is a difference in the taste of the two sauces.

Answer 1

To test against

Here

sample mean of difference

sample standard deviation of difference

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 5% level of significance if

Now,

The value of the test statistic

and critical value

and P-value

Since and P-value = 0.0218664 < 0.05, so we reject H₀ at 5% level of significance and we can conclude that there is significant difference in the taste of the two sauces.