A researcher employed by a university dining facility wanted to know whether din
ID: 3317494 • Letter: A
Question
A researcher employed by a university dining facility wanted to know whether dining-facility customers like gingerbread cookies less than Russian teacakes (a type of hazelnut cookie coated with confectioner’s sugar). To investigate this, consecutive dining-facility customers were given a free cookie—either a gingerbread cookie or a Russian tea cake—and were asked to rate liking for the cookie on a scale of 0 (“hated it”) to 10 (“loved it”).
d) With = .025, (i) decide whether to retain or to reject the null hypothesis, and (ii) explain your decision by describing the relationship of P and .025 (i.e., >, <, =, , etc.). (Your answer should respond to both i and ii.)
e) Suppose that the randomization process had not been constrained so that an equal number of participants would rate each cookie, and that instead the numbers of participants who rated each cookie was as shown in the table for part e, but that everything else was the same (i.e., the means and standard deviations are as shown in the table). Calculate the two-sample t statistic, indicate the number of degrees of freedom (using Option 2), obtain a P-value, and, with = .025, decide whether to reject the null hypothesis.
f) Suppose that the randomization process had not been constrained so that an equal number of participants would rate each cookie, and that instead the numbers of participants who rated each cookie was as shown in the table for part e, but that everything else was the same (i.e., the means and standard deviations are as shown in the table). Calculate the two-sample t statistic, indicate the number of degrees of freedom (using Option 2), obtain a P-value, and, with = .025, decide whether to reject the null hypothesis.
g) If you have done parts e, and f correctly, you should see at least two reasons why, in an experiment with two conditions, you are best off with the sample divided equally between the two conditions. What are they?
group Cookie N (for parts c and d) Mean SD N (for part e) N (for part f) 1 Gingerbread 21 6.34 2.13 30 12 2 Russian teacake 21 8.02 2.26 12 30Explanation / Answer
Part D
p-value = 0.0087
As p-value is less than significance level of 0.025, we reject the null hypothesis.
Part E
p-value = 0.0197
As p-value is less than significance level of 0.025, we reject the null hypothesis.
part F
p-value = 0.0169
As p-value is less than significance level of 0.025, we reject the null hypothesis.
Given Data Sample 1 Sample 2 Name Gingerbread Russian teacake mean 6.34 8.02 Sample size 21 21 Std. dev. 2.13 2.26Related Questions
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