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. Random samples of 69 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¯ = -0.46731 with a standard deviation of s_d = 1.65540. Use α = 0.05. (Hint: A 2-sample dependent means test is the same as what type of test?)

(a) Choose the appropriate hypotheses for a two-tailed test. Assume μ_d is the average difference in the 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 t_calc. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)

t_calc            

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

p-value            

(e) State your conclusion.

We (Click to select)cancannot conclude that there is a difference in the taste of the two sauces.

Answer 1

Solution:

Sample size,n=69

Sample mean,=-0.46731

Sample standard deviation,sd=1.65540

Level of significance,=0.05

Degree of freedom, df=n-1=69-1=68

a)The appropriate hypothesis for a two-tailed test to test whether the μd is the average difference in the taste of the two sauces is

Null Hypothesis:H0: μd = 0 versus Alternative Hypothesis:H1: μd ≠ 0

b)The t-test statistics is calculated as follows:

tcalc= / sd/n

=-0.46731 /  1.65540/69

=-2.331

Thus, the test statistics value is -2.331

c)P-value from the t-distribution table for n=69 is 0.0227

d)The t-critical value from the t-distribution table for df=68 and /2=0.025 is 2.292

Since tcalc=2.331 is greater than the t- critical value=2.292, we reject the null hypothesis.