1.4 HW stats

Student researchers were interested in whether people will be more likely to choose the name-brand cookie (Chips Ahoy) over the store-brand (Chipsters) in a blind taste test. They tested this with 20 subjects and found that 14 (70%) chose Chips Ahoy as their favorite. They conducted a test of significance using simulation and got the following null distribution. (Note that this null distribution uses only 100 simulated samples and not the usual 1,000 or 10,000.) We will let π represent the long-run proportion of students that pick Chips Ahoy as their favorite. a. Set up the correct the null and alternative hypotheses in symbols for the research question, "Do a majority of students prefer Chips Ahoy over Chipsters?"

H0: π = 0.50 Ha: π > 0.50

c. Set up the correct the null and alternative hypotheses in symbols for the research question, "Do students have a preference between Chips Ahoy and Chipsters?"

H0: π = 0.50 Ha: π ≠ 0.50

b. You increase the sample size and still find a sample proportion of 0.68. The new standardized statistic will be ___ because ____

larger ( farther from zero), it is less likely to get extreme values of the statistic from a larger sample

Suppose you are testing the hypotheses H0: π = 0.50 versus Ha: π > 0.50. You get a sample proportion of 0.68 and find that your p-value is 0.02. Now suppose you redid your study with each of the following changes, will your new p-value be larger, smaller, or stay the same as the 0.02 you first obtained? Be sure to explain your reasoning. a. Keeping the sample size the same, you take a new sample and find a sample proportion of 0.66. The new p-value will be ____ because _____

larger, the sample proportion is closer to the hypothesized long-run proportion value of 0.50

c. You decide to use a two-sided alternative hypothesis (Ha: π ≠ 0.50). The new p value will be ____ because

not the same, not because the sample proportion did not change not the p value calculation is the same in one sided and two sides tests

b. Using the null distribution above, what is the p-value when testing the hypotheses in part (a)?

p-value = 3/100 = 0.03

d. Using the null distribution above, what is the p-value when testing the hypotheses in part (c)?

p-value = 8/100 = 0.08

Suppose you are testing the hypotheses H0: π = 0.50 versus Ha: π > 0.50. You get a sample proportion of 0.68 and find that your standardized statistic is 2.53. Now suppose you redid your study with each of the following changes; will your new standardized statistic be larger, smaller, or stay the same as the 2.53 you first obtained? Explain your reasoning. a. Keeping the sample size the same, you take a new sample and find a sample proportion of 0.66. The standardized statistic will be ___ because ____

smaller (closer to zero), the sample proportion is closer to the hypothesized long run proportion value of 0.5

b. You increase the sample size and still find a sample proportion of 0.68. The new p value will be ____ because _____

smaller, it is less likely to get extreme values of the statistic from a larger sample

c. You decide to use a two-sided alternative hypothesis (Ha: π ≠ 0.50). The new standardized statistic will be ____ because _____

the same, the sample proportion is still the same distance away from the center of the null distribution