Self test on chapter 18 sampling distributions

1. Self test on chapter 18 sampling distributions

2. Problem 1a It is generally believed that electrical problems affect about 14% of new cars. An automobile mechanic conducts diagnostic tests on 128 new cars on the lot. • Describe the sampling distribution for the proportion of cars with electrical problems. [Name the model and state the parameters.] We can assume that these cars a representative sample of all new cars and certainly less than 10% of the population of new cars. Also, np = 17.92 and nq = 110.08, both more than 10. Therefore, the sample proportions here are Normally distributed with mean p = 0.14 and standard deviation of 0.031.

3. Problem 1b It is generally believed that electrical problems affect about 14% of new cars. An automobile mechanic conducts diagnostic tests on 128 new cars on the lot. • Sketch and clearly label the model. The sampling distribution of p-hat

4. Problem 1c It is generally believed that electrical problems affect about 14% of new cars. An automobile mechanic conducts diagnostic tests on 128 new cars on the lot. • The mechanic finds that in this group, 18% of the new cars have electrical problems. Is that unusual? or about 10%. So it’s not that unusual.

5. Problem 2 Herpetologists found that a certain species of python have an average length of 20.5 feet with a standard deviation of 2.3 feet. Later the scientists collected a random sample of 30 pythons and measured their lengths. The mean length for the sample was 19.5 feet long. One of the herpetologists fears that pollution might be affecting the natural growth of the pythons. Is this sample value cause for concern? Even though we don’t know the population distribution of python lengths, we have a random sample of pythons and a sample size of 30. The Central Limit Theorem says that the sampling model is approximately N(20.5, 0.42). A sample mean of 19.5 is more than 2 standard deviations below the mean. So it is unusual (p = .0086)