Download Inference About the Mean of a Population - Chapter 13, 14 | MATH 1530 and more Exams Statistics in PDF only on Docsity! Math 1530 Name _________________________ Chapters 13 & 14 . Inference about the mean of a population. 1. Company SUCCESS-2000 advertises that by using its program, high school students can increase their Verbal SAT scores. A high school teacher is skeptical of this claim. She suspects the average score will be the same and there will be no increase. The teacher plans to examine data from a sample of students who use the program to see if the claim is true. If represents the mean increase in Verbal SAT score if all high school students used the method, the null and the alternative hypotheses are: A) Ho: < 0 and Ha: =0 B) Ho: = 0 and Ha: >0 C) Ho: = 0 and Ha: <0 D) Ho: = 0 and Ha: 0 E) Ho: 0x and Ha: 0x 2. In a given situation, the consequences of Type I error are extremely serious. What do you advice? A) To choose =0.95 B) To choose a very small alpha ( ) C) To choose smaller than the p-value D) To choose =0.1 E) Choose p-value 0.01 3. We carry out a hypothesis test of the hypotheses: H0: =0 and Ha: > 0 and obtain a P-value of 0.002. Which is the correct interpretation of that value? A) The chance that the null hypothesis is true is 0.002. B) The chance that the alternative hypothesis is true is 0.998. C) The chance of obtaining a value of the test statistic as or larger than the value actually obtained if H0 is true is 0.002. D) The chance of obtaining a value of the test statistic > 0 is only 0.002 E) The chance that the alternative hypothesis is true is 0.002 Questions 4,5 & 6 refer to the following case: A particular model car advertises that it gets 30 miles per gallon in city driving. A consumer group wishes to see if this is true or if the gas mileage is lower than 30 miles per gallon. They try a sample of 4 cars of this model, and find the gas mileage of each car after 15,000 miles of city driving. They compute the mean gas mileage for the 4 cars and find it to be x = 27.5 miles per gallon. Assume the distribution of city gas mileage of cars is normal with mean and standard deviation =2 miles per gallon. Consider H0: = 30 Ha: < 30 4. Calculate the p-value. A) 2.5 B) -2.5 C) 0.99379 D)0.0062 E) -1.25 5. Assume that we want to work with =0.05. What would be the appropriate conclusion? A) The advertisement is correct, that model has a mileage of 30 miles per gallon B) The advertisement is wrong, the mileage is under 30 miles per gallon C) We can not arrive at a conclusion because we have not tried all the cars D) We reject the alternative hypothesis because the p-value is negative E) The mileage for the population of all cars of that type is 27.5 miles per gallon 6) In a test of hypothesis we decided to make =0.05. The p-value was 0.136 Which would be the correct decision? A) Reject the null hypothesis B) Do not reject the null hypothesis C) Change the to 0.3 D) The results are inconclusive E) The results are significant at the 0.05 level
