- Viii A Researcher Employed By A University Dining Facility Wanted To Know Whether Customers Like Russian Teacakes A Ty 1 (55.5 KiB) Viewed 32 times
- Viii A Researcher Employed By A University Dining Facility Wanted To Know Whether Customers Like Russian Teacakes A Ty 2 (15.61 KiB) Viewed 32 times
- Viii A Researcher Employed By A University Dining Facility Wanted To Know Whether Customers Like Russian Teacakes A Ty 3 (96.53 KiB) Viewed 32 times
VIII. 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 Mean SD n (for (for part 5) (for part 6) parts 3 and 4) n n 1 Gingerbread 41 6.29 1.92 77 5 2 Russian teacake 41 7.26 2.23 5 77
4) With a = .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., >,<=, H, etc.). (Your answer should respond to both i and ii.)
Parts ) and 6 are repetitious and tedious, but it 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 a = .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). (1) 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 a = 025, decide whether to reject the null hypothesis. Be sure to do each of these four things. 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?