A chi-square goodness-of-fit test is used to test whether a 0 to 9 spinner is "fair" (that is, the outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded. The degrees of freedom for the test will be
(a) 8 .
(c) 10 .
(e) None of these.
(b) 9 .
(b) The degrees of freedom for the test is .
Need to find the degrees of freedom for the test.
We have been given a 0 to 9 spinner, which has 10 possible outcomes:
This then implies that there are 10 possible categories for the variables.
The degrees of freedom for the (chi-square goodness-of-fit) test is then the number of categories decreased by
Gastric freezing was once a recommended treatment for ulcers in the upper intestine. The use of gastric freezing stopped after experiments showed it had no effect. One randomized comparative experiment found that of the gastric-freezing patients improved, while of the patients in the placebo group improved. We can test the hypothesis of “no difference” in the effectiveness of the treatments in two ways: with a two-sample z test or with a chi-square test.
(a) Minitab output for a chi-square test is shown below. State appropriate hypotheses and interpret the P-value in context. What conclusion would you draw?
Chi-Square Test: Gastric freezing, Placebo Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts
(b) Minitab output for a two-sample z test is shown below. Explain how these results are consistent with the test in part (a).
After randomly assigning subjects to treatments in a randomized comparative experiment, we can compare the treatment groups to see how well the random assignment worked. We hope to find no significant differences among the groups. A study on how to provide premature infants with a substance essential to their development assigned infants at random to receive one of four types of supplements, called PBM, NLCP, PL-LCP, and TG-LCP. The subjects were premature infants. In the experiment, were assigned to the PBM group and to each of the other treatments.
(a) The random assignment resulted in females in the TG-LCP group and 11 females in each of the other groups. Make a two-way table of the group by gender. Calculate the proportion of females in each treatment group. Does it appear that the random assignment roughly balanced the groups by gender? Explain.
(b) Are the differences between the groups statistically significant? Give appropriate evidence to support your answer.
Seagulls by the seashore Do seagulls show a preference for where they land? To answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore whose area was made up of % sand, % mud, and % rocks. The biologists chose seagulls at random. Each seagull was released into the outdoor space on its own and observed until it landed somewhere on the piece of shore. In all, seagulls landed on the sand, role="math" localid="1650465230449" landed in the mud, and role="math" localid="1650465221489" landed on the rocks. Carry out a chi-square goodness-of-ﬁt test. What do you conclude?
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