RagingRaccoon
04-21-2008, 11:44 PM
Hi, Im kind of freaking out due to this test tomorrow. For some reason I cannot teach myself this stuff, I did just fine last test teaching myself but this time around isnt really working for me. Here are the questions: Any help would be great, thank you. I do have messengers if that would help, thank you.
Review 3
STAT 330
1. An insurance company wants to estimate the average repair cost to compact cars damaged in low-speed, rear-impact collisions. A random sample of 25 cars with this type of damage resulted in an average repair cost of X= $972.36 with a standard deviation of s = $82.35.
a. Identify the population and the population parameter of interest in this problem.
b. Find a 95% confidence interval for the mean repair cost for compact cars damaged in low-speed, rear-impact collisions based on this sample.
c. Interpret the above interval in terms of this problem.
2. Two candidates, Roy and Shirley, are running for the same state office. A newspaper wants to determine what proportion of likely voters will vote for Roy. A SRS of 500 likely voters were asked who they will vote for and 260 out of the 500 voters said they will vote for Roy.
a. Identify the population and the population parameter of interest in this problem.
b. Find a 95% confidence interval for the proportion of voters who will vote for Roy.
c. Interpret this interval in terms of this problem.
d. Based on your interval in part (b), can Roy be sure of winning?
e. Find the sample size needed to guarantee that we can estimate a population proportion to within 0.025 using a 95% confidence interval.
3. A farmer is trying to sell a truckload of potatoes to a company that makes potato chips. Before the company agrees to buy a load of potatoes, a sample of potatoes is tested for quality to determine whether the load is acceptable for making chips. If the sample fails this test, the load will be rejected. They are essentially testing the following hypotheses:
H0 : The load of potatoes is acceptable.
HA : The load is not acceptable.
a. What would be the type I error and its consequence in this situation?
b. What would be the type II error and its consequence in this situation?
c. The farmer suspects that his potatoes may have gone bad during shipment, but would still like to sell them. Would he hope the test had high or low power? Explain.
d. The company’s accountant has complained that they are purchasing too many bad potatoes. Would he argue for a larger or smaller α? Explain.
4. The brochure for graduate study at a large research university states that the average amount the university’s graduate students spend on rent is $400 per month. A new graduate student has arrived on campus and almost every apartment she has looked at has a rent considerably larger than $400 per month. She believes that the brochure is misleading and that the actual average rent paid by graduate
1/2
2/2
students is much larger. To test this, she asked 19 graduate students in her department how much each pays in rent. This sample had a mean of $441.60 and a standard deviation of $85.25.
a. Identify the population and population parameter of interest above.
b. State the hypotheses needed to test the student’s claim.
c. Based on the student’s sample, calculate the appropriate test statistic to perform the hypothesis test above.
d. Based on the test statistic above, state a conclusion in terms of this problem at the 5% significance level.
e. This student has never taken a statistics course. If she had (and passed),
what is the one thing she should have done differently?
5. A statistics professor thinks that over 30% of all the cars parked at NDSU have the university’s logo on them. He had his students take a random sample of 500 cars parked on campus and they observed 164 cars with the logo. Identify the population and population parameter of interest and then test the professor’s claim at the 5% significance level.
6. Each of the following situations involves a hypothesis test that compares means. For each situation, identify whether a one-sample, matched-pairs, or two-sample design was used.
a. A researcher wants to study whether noise affects reading comprehension. She has a sample of 12 students. Each student will take two similar tests of reading comprehension. In random order, one test will be taken in a room that is relatively quiet and the other in a room with loud music and crowd noise.
b. Some statistics students at NDSU want to determine whether the prices for textbooks at the NDSU Bookstore and Amazon.com are basically the same, on average. One group of students found the prices of a random selection of 30 books at the NDSU Bookstore and another group found the prices of 35 different books at Amazon.com.
c. Suppose that a government official believes that medical doctors receiving their degrees this year have, on average, over $100,000 in student loans. To test this, the official obtained a random sample of 25 of these new doctors and found out how much in student loans each owed.
d. Two researchers believe that students at NDSU take fewer credits during spring semester, on average, than during fall semester. They randomly selected 50 students at NDSU and asked them how many credits they took in fall and how many credits they took in spring.
e. Some statistics students want to know which of two pizza restaurants has the faster average delivery time on Friday nights just after midnight. From each of six different houses (on six different Friday nights), they ordered a large pepperoni pizza from both restaurants. They then measured the length of time it took for the pizzas to be delivered.
Review 3
STAT 330
1. An insurance company wants to estimate the average repair cost to compact cars damaged in low-speed, rear-impact collisions. A random sample of 25 cars with this type of damage resulted in an average repair cost of X= $972.36 with a standard deviation of s = $82.35.
a. Identify the population and the population parameter of interest in this problem.
b. Find a 95% confidence interval for the mean repair cost for compact cars damaged in low-speed, rear-impact collisions based on this sample.
c. Interpret the above interval in terms of this problem.
2. Two candidates, Roy and Shirley, are running for the same state office. A newspaper wants to determine what proportion of likely voters will vote for Roy. A SRS of 500 likely voters were asked who they will vote for and 260 out of the 500 voters said they will vote for Roy.
a. Identify the population and the population parameter of interest in this problem.
b. Find a 95% confidence interval for the proportion of voters who will vote for Roy.
c. Interpret this interval in terms of this problem.
d. Based on your interval in part (b), can Roy be sure of winning?
e. Find the sample size needed to guarantee that we can estimate a population proportion to within 0.025 using a 95% confidence interval.
3. A farmer is trying to sell a truckload of potatoes to a company that makes potato chips. Before the company agrees to buy a load of potatoes, a sample of potatoes is tested for quality to determine whether the load is acceptable for making chips. If the sample fails this test, the load will be rejected. They are essentially testing the following hypotheses:
H0 : The load of potatoes is acceptable.
HA : The load is not acceptable.
a. What would be the type I error and its consequence in this situation?
b. What would be the type II error and its consequence in this situation?
c. The farmer suspects that his potatoes may have gone bad during shipment, but would still like to sell them. Would he hope the test had high or low power? Explain.
d. The company’s accountant has complained that they are purchasing too many bad potatoes. Would he argue for a larger or smaller α? Explain.
4. The brochure for graduate study at a large research university states that the average amount the university’s graduate students spend on rent is $400 per month. A new graduate student has arrived on campus and almost every apartment she has looked at has a rent considerably larger than $400 per month. She believes that the brochure is misleading and that the actual average rent paid by graduate
1/2
2/2
students is much larger. To test this, she asked 19 graduate students in her department how much each pays in rent. This sample had a mean of $441.60 and a standard deviation of $85.25.
a. Identify the population and population parameter of interest above.
b. State the hypotheses needed to test the student’s claim.
c. Based on the student’s sample, calculate the appropriate test statistic to perform the hypothesis test above.
d. Based on the test statistic above, state a conclusion in terms of this problem at the 5% significance level.
e. This student has never taken a statistics course. If she had (and passed),
what is the one thing she should have done differently?
5. A statistics professor thinks that over 30% of all the cars parked at NDSU have the university’s logo on them. He had his students take a random sample of 500 cars parked on campus and they observed 164 cars with the logo. Identify the population and population parameter of interest and then test the professor’s claim at the 5% significance level.
6. Each of the following situations involves a hypothesis test that compares means. For each situation, identify whether a one-sample, matched-pairs, or two-sample design was used.
a. A researcher wants to study whether noise affects reading comprehension. She has a sample of 12 students. Each student will take two similar tests of reading comprehension. In random order, one test will be taken in a room that is relatively quiet and the other in a room with loud music and crowd noise.
b. Some statistics students at NDSU want to determine whether the prices for textbooks at the NDSU Bookstore and Amazon.com are basically the same, on average. One group of students found the prices of a random selection of 30 books at the NDSU Bookstore and another group found the prices of 35 different books at Amazon.com.
c. Suppose that a government official believes that medical doctors receiving their degrees this year have, on average, over $100,000 in student loans. To test this, the official obtained a random sample of 25 of these new doctors and found out how much in student loans each owed.
d. Two researchers believe that students at NDSU take fewer credits during spring semester, on average, than during fall semester. They randomly selected 50 students at NDSU and asked them how many credits they took in fall and how many credits they took in spring.
e. Some statistics students want to know which of two pizza restaurants has the faster average delivery time on Friday nights just after midnight. From each of six different houses (on six different Friday nights), they ordered a large pepperoni pizza from both restaurants. They then measured the length of time it took for the pizzas to be delivered.