Question

You are on the market for a new car. You want to check whether there is a significant difference between the fuel economy of mid-size domestic cars and mid-size import cars. You sample 24 domestic car makes and find an average fuel economy of 30.169 MPG with a standard deviation of 4.9556 MPG. For imports, you sample 14 cars and find an average MPG of 36.638 MPG with a standard deviation of 7.6187. Construct a 90% confidence interval for the difference between the true average fuel economies in question. Assume the difference will represent (domestic - import). You can also assume that the standard deviations are statistically the same between the two populations.

2.

A pharmaceutical company is testing a new drug to increase memorization ability. It takes a sample of individuals and splits them randomly into two groups. After the drug regimen is completed, all members of the study are given a test for memorization ability with higher scores representing a better ability to memorize. Those 20 participants on the drug had an average test score of 28.062 (SD = 4.642) while those 24 participants not on the drug had an average score of 46.056 (SD = 6.934). You use this information to create a 95% confidence interval for the difference in average test score. What is the margin of error? Assume the population standard deviations are equal.

3. A professor at a university wants to estimate the average number of hours of sleep students get during exam week. The professor wants to find a sample mean that is within 1.117 hours of the true average for all college students at the university with 99% confidence. If the professor knows the standard deviation of the sleep times for all college students is 4.067, what sample size will need to be taken?

4. The owner of a local golf course wants to determine the average age of the golfers that play on the course in relation to the average age in the area. According to the most recent census, the town has an average age of 48.89. In a random sample of 24 golfers that visited his course, the sample mean was 31.37 and the standard deviation was 9.976. Using this information, the owner calculated the confidence interval of (25.65, 37.09) with a confidence level of 99%. Which of the following statements is the best conclusion?

5. You own a small storefront retail business and are interested in determining the average amount of money a typical customer spends per visit to your store. You take a random sample over the course of a month for 42 customers and find that the average dollar amount spent per transaction per customer is $89.687 with a standard deviation of $10.9431. When creating a 99% confidence interval for the true average dollar amount spend per customer, what is the margin of error?

Answer 1

Problem 1 solved.

You are on the market for a new car. You want to check whether there is a significant difference between the fuel economy of mid-size domestic cars and mid-size import cars. You sample 24 domestic car makes and find an average fuel economy of 30.169 MPG with a standard deviation of 4.9556 MPG. For imports, you sample 14 cars and find an average MPG of 36.638 MPG with a standard deviation of 7.6187. Construct a 90% confidence interval for the difference between the true average fuel economies in question. Assume the difference will represent (domestic - import). You can also assume that the standard deviations are statistically the same between the two populations.

Population 1 Sample
Sample Size	24
Sample Mean	30.169
Sample Standard Deviation	4.9556
Population 2 Sample
Sample Size	14
Sample Mean	36.638
Sample Standard Deviation	7.6187
Intermediate Calculations
Population 1 Sample Degrees of Freedom	23
Population 2 Sample Degrees of Freedom	13
Total Degrees of Freedom	36
Pooled Variance	36.6504
Standard Error	2.0359
Difference in Sample Means	-6.4690

Confidence Interval Estimate
for the Difference Between Two Means
Data
Confidence Level	90%
Intermediate Calculations
Degrees of Freedom	36
t Value	1.6883
Interval Half Width	3.4372
Confidence Interval
Interval Lower Limit	-9.9062
Interval Upper Limit	-3.0318

90% confidence interval for the difference between the true average fuel economies = (-9.9062, -3.0318).

The 90% CI does not contain 0 value. Therefore we conclude that there is a significant difference between the fuel economy of mid-size domestic cars and mid-size import cars at 90% confidence level.