You are testing against based on an SRS of
observations from a Normal population. What values of the t statistic are statistically significant at the level?
The correct option is (d)
Level of significance
The null and alternative hypotheses are:
The degree of freedom is:
The critical value at a significance level and degrees of freedom can be calculated using the critical value table as follows:
The test would be significant for the values or
Hence, the correct option is (d).
Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than 5% of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000 adults.
a. State appropriate hypotheses for testing the company’s claim. Be sure to define your parameter.
b. Describe a Type I error and a Type II error in this setting, and give the consequences Page Number: 615 of each.
c. Would you recommend a significance level of 0.01, 0.05, or 0.10 for this test? Justify your choice.
d. The power of the test to detect the fact that only 3% of adults who use this vaccine would develop flu using α=0.05 is 0.9437. Interpret this value.
e. Explain two ways that you could increase the power of the test from part (d).
Significance tests A test of versus based on
a sample of size yields the standardized test statistic . Assume that the conditions for performing inference are met.
a. Find and interpret the P-value.
b. What conclusion would you make at the significance level? Would
your conclusion change if you used α=0.05 instead? Explain your reasoning.
c. Determine the value of p^= the sample proportion of successes.
Better parking A local high school makes a change that should improve student
satisfaction with the parking situation. Before the change, of the school’s students approved of the parking that was provided. After the change, the principal surveys an SRS of from the more than students at the school. In all, students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective.
a. Describe a Type I error and a Type II error in this setting, and give a possible
consequence of each.
b. Is there convincing evidence that the principal’s claim is true?
Walking to school A recent report claimed that of students typically walk to school. DeAnna thinks that the proportion is higher than at her large elementary school. She surveys a random sample of students and finds that typically walk to school. DeAnna would like to carry out a test at the significance level of versus , where = the true proportion of all students at her elementary school who typically walk to school. Check if the conditions for performing the significance test are met.
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