12 May 1. In order to rule on a potential federal grant, a government official
1. In order to rule on a potential federal grant, a government official must confirm that the average income in a Pennsylvania county is less than $12,500. A sample of 35 individuals is taken and shows a sample mean of $10,950 and a sample standard deviation of $3,972. Conduct the test at a 5%(0.05) level of significance. What is your conclusion? 2. From a population of cans of coffee marked “12 ounces”, a random sample of 41 cans was selected and the contents of each can were weighed. The sample revealed a mean of 11.80 ounces and a sample standard deviation of 0.5 ounces. At a 1%(0.01) level of significance, test to see if the mean of the population differs from 12 ounces. What is your Conclusion? 3. A presidential candidate has decided to enter primaries in those states in which at least 20% of voters support her. Random samples of 200 voters were taken in each of a number of states. In New Hampshire, 33 voters supported the candidate. Test at a 5%(0.05) level of significance to determine whether the candidate should enter the New Hampshire primary. What is the p-value for this test? What is your conclusion? 4. Samples of final examination scores for two statistics classes with different instructors provided the following results: For instructor “A” the sample size was 12, the sample mean score was 72 and the sample standard deviation was 6. For instructor “B” the sample size was 15, the sample mean score was 78 and the sample standard deviation was 8. At a 5%(0.05) level of significance, test whether these data are sufficient to conclude that the mean scores for the two classes are the same? What is your conclusion? 5. In a random sample of 200 Republicans,155 indicated they opposed the new tax law proposal. While in a random sample of 120 Democrats, 84 opposed the tax law. At a 5%(0.05) level of significance, test to determine if there is a significant difference in the proportion of Republicans and Democrats opposed to this new law. What is your conclusion? 6. For Problem #3 above concerning the presidential candidate: (A) What would be the consequence of making a Type I error? (B) What would be the consequence of making a Type II error?
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