A researcher employed by a university dining facility wanted to know whether customers like Russian teacakes (a type of nut cookie coated with confectioner’s sugar) more than gingerbread cookies. More formally, the researcher wanted to know
whether, for dining facility customers, the population mean liking for Russian teacakes is greater than that for
gingerbread cookies. To investigate this, dining-facility customers were given a free cookie—either a gingerbread cookie or a
Russian teacake—and were asked to rate their liking for the cookies using a scale of 0 (“hated it”) to 10 (“loved it”). The
results are summarized in the table below. (31 pts.—3/3/8/2/6/6/3)
Group Cookie n
(for parts 3
and 4)
Mean SD n
(for part 5)
n
(for part 6)
B
1 Gingerbread 41 6.29 1.92 75 7
2 Russian teacake 41 7.26 2.23 7 75
C
1 Gingerbread 31 6.48 1.88 56 6
2 Russian teacake 31 7.58 2.12 6 56
1) Referring carefully to the description of the study, specify the null and alternative hypotheses that are being tested. These
hypotheses should be about two population means that you will define in part 2.
2) Your hypotheses should contain two µs; define what these are. Your definitions should be of the form “μ1 is the population
mean taste rating for ; μ2 is the population mean taste rating for ___”, in which the blanks are filled in appropriately.
3) Assume that cookies were assigned to customers randomly but with equal numbers of customers getting each cookie.
Using information from the line in the table assigned to you, using the sample sizes (n) for parts 3 and 4, (i) calculate a
two-sample t statistic; (ii) indicate the number of degrees of freedom of the t statistic using Option 2 (Moore et al., The
Basic Practice of Statistics); and (iii) find the P value (saying whether the P value is one-sided or two-sided). (Use either a
table of critical values of t to give an approximate P value or technology to find an exact P.) (Be sure to do each of these
things.)
4) With α = .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.)
Parts 5 and 6 are repetitious and tedious, but if done correctly, teach an important lesson…
5) 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 5. Suppose
that everything else was the same (i. e., the sample means and standard deviations are as shown in the table). (i) Calculate
the two-sample t statistic, (ii) indicate the number of degrees of freedom (using Option 2), (iii) obtain a P-value, saying
whether the P-value is one-sided or two-sided, and (iv) with α = .025, decide whether to reject the null hypothesis. Be sure
to do each of these four things.
6) 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 6. Suppose
that everything else was the same (i. e., the sample means and standard deviations are as shown in the table). (i) Calculate
the two-sample t statistic, (ii) indicate the number of degrees of freedom (using Option 2), (iii) obtain a P-value, saying
whether the P-value is one-sided or two-sided, and (iv) with α = .025, decide whether to reject the null hypothesis.
7) If you have done parts 3, 5, and 6 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?