all adults use alcoholic beverages. (E) None of these 57. A researcher wished to

Question

all adults use alcoholic beverages. (E) None of these 57. A researcher wished to test the effect of the addition of extra calcium to yogurt on the "tastiness" of yogurt. The "tastiness" was measured on the scales 1 to 10, 1 being "very unpleasant" and 10 being "very pleasant". A mean rating for 16 randomly selected adults who tasted yogurt containing the extra calcium was 6.5 with a standard deviation of 1.5. An independent random sample of 14 adults who tasted yogurt without the added calcium gave a mean rating of 7 with a standard deviation of 2. The distribution of ratings for "tastiness" of yogurt with and without the added calcium follows approximately normal distribution with equal variances. At a 10% significance level, does the data provide sufficient evidence to support the claim that the mean rating of the "tastiness" is significantly lower for the yogurt with the added calcium? What is the appropriate p-value? (B) 0.2257 (C) 0.7743 (D) 0.7792 (E) None of these

Explanation / Answer

The statistical software output for this problem is:

Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 < 0
(with pooled variances)

Hypothesis test results:

Hence,

P - value = 0.2208

Option A is correct.

Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 -0.5 0.64043442 28 -0.78072006 0.2208

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