# STAT-2160-145 Homework 6 Business Statistics Option 4

**Question 1**

A professor at a university wants to estimate the average number of hours of sleep students get during exam week. On the first day of exams, she asked 28 students how many hours they had slept the night before. The average of the sample was 4 with a standard deviation of 1.484. When estimating the average amount of sleep with a 95% confidence interval, what is the margin of error?

1) 0.4777

2) 0.5754

3) 0.5745

4) 0.3298

5) 0.2804

**Question 2**

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 11 customers and find that the average dollar amount spent per transaction per customer is $114.645 with a standard deviation of $18.2388. Create a 90% confidence interval for the true average spent for all customers per transaction.

1) ( 104.768 , 124.522 )

2) ( 112.833 , 116.457 )

3) ( 104.678 , 124.612 )

4) ( -104.678 , 124.612 )

5) ( 109.146 , 120.144 )

**
Question 3
**The owner of a local phone store wanted to determine how much customers are willing to spend on the purchase of a new phone. In a random sample of 14 phones purchased that day, the sample mean was $368.758 and the standard deviation was $23.8051. Calculate a 95% confidence interval to estimate the average price customers are willing to pay per phone.

1) ( 366.598 , 370.918 )

2) ( 355.111 , 382.405 )

3) ( -355.013 , 382.503 )

4) ( 362.396 , 375.12 )

5) ( 355.013 , 382.503 )

**Question 4**

In a climate survey, it was determined that in a random sample of 15 days, the average temperature in Kalamazoo at 2:00 PM in the months of July and August is 73.38 degrees with a standard deviation of 3.798 degrees. Using this information, a 95% confidence interval for the average is (71.28, 75.48). Which of the following is the appropriate interpretation of this interval?

1) We cannot determine the proper interpretation of this interval.

2) We are certain that 95% of the days in the months of August and July will have a temperature at 2:00 PM between 71.28 and 75.48.

3) We are 95% confident that the average daily temperature for the months of July and August at 2:00 PM for the days recorded is between 71.28 and 75.48.

4) We are 95% confident that the average daily temperature for the months of July and August at 2:00 PM is between 71.28 and 75.48.

5) We are 95% confident that the proportion of all days’ temperatures will fall between 71.28 and 75.48.

**Question 5**

**t**Suppose that you are the director of table game operations at a large casino, known especially for its poker room. You are interested in determining the average number of hands the casino should expect per hour during peak hours in the poker room. You monitor the number of hands over the next week and given a random sample of 27 hours, you see that on average 188.6 hands are played per hour, with a standard deviation of 9.24 hands and you calculated a 90% confidence interval to be (185.6, 191.6). Your manager believes the true mean is 150.5. Which of the following is the best conclusion?

1) We are 90% confident that the average number of hands played per hour is greater than 150.5.

2) The average number of hands played per hour is not significantly different from 150.5

3) The percentage of hours in which more than 150.5 hands of poker are played is 90%.

4) We are 90% confident that the average number of hands played per hour is less than 150.5.

5) We cannot determine the proper interpretation based on the information given.

**Question 6**

As an avid golfer, you want to estimate your average score for 18 holes of golf. Suppose you know that the standard deviation of your score is 24.329 strokes and you want to find a sample mean that is within 6.127 strokes of your true average for all rounds of golf with 90% confidence. How many rounds would you need to play to determine this?

1) 42

2) We do not have enough information to answer this question since we were not given the sample mean.

3) 53

4) 48

5) 43

**Question 7**

In a consumer research study, several Meijer and Walmart stores were surveyed at random and the average basket price was recorded for each. It was found that the average basket price for 36 Meijer stores was $62.613 with a standard deviation of $10.724. Similarly, 58 Walmart stores had an average basket price of $62.471 with a standard deviation of $14.703. If a 99% confidence interval for the difference between the true average basket prices of Meijer versus Walmart is calculated, what is the margin of error? You can assume that the standard deviations of the two populations are statistically similar.

1) 7.439

2) 6.696

3) 2.82831539

4) 2.63032961

5) 7.285

**Question 8**

The owner of a local supermarket wants to estimate the difference between the average number of gallons of milk sold per day on weekdays and weekends. The owner samples 9 weekdays and finds an average of 222.41 gallons of milk sold on those days with a standard deviation of 32.336. 9 (total) Saturdays and Sundays are sampled and the average number of gallons sold is 374.33 with a standard deviation of 47.147. Construct a 90% confidence interval to estimate the difference of (average number of gallons sold on weekdays – average number of gallons sold on weekends). Assume the population standard deviations are the same for both weekdays and weekends.

1) (-183.27, -120.57)

2) (-185.19, -118.65)

3) (-1496.92, 1193.08)

4) (-170.98, -132.86)

5) We only have the sample means, we need to know the population means in order to calculate a confidence interval.

**Question 9**

It is believed that using a solid state drive (SSD) in a computer results in faster boot times when compared to a computer with a traditional hard disk (HDD). You sample a group of computers and use the sample statistics to calculate a 99% confidence interval of (1.12, 10.49). This interval estimates the difference of (average boot time (HDD) – average boot time (SSD)). What can we conclude from this interval?

1) There is no significant difference between the average boot time for a computer with an SSD drive and one with an HDD drive at 99% confidence.

2) We do not have enough information to make a conclusion.

3) We are 99% confident that the difference between the two sample means falls within the interval.

4) We are 99% confident that the average boot time of all computers with an SSD is greater than the average of all computers with an HDD

5) We are 99% confident that the average boot time of all computers with an HDD is greater than the average of all computers with an SSD.

**Question 10**

You are in 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 23 domestic car makes and find an average fuel economy of 31.481 MPG with a standard deviation of 3.473 MPG. For imports, you sample 14 cars and find an average MPG of 36.512 MPG with a standard deviation of 6.326. You use this information to calculate a 99% confidence interval for the difference in mean fuel economy of (-9.406, -0.656). Of the following statements, what is the best interpretation of this interval?

1) We are 99% sure that the average difference in fuel economy of all domestic cars and all import cars is between -9.406 and -0.656.

2) We are 99% confident that the difference between the average fuel economy of all domestic mid-size cars and all import mid-size cars surveyed is between -9.406 and -0.656.

3) We are certain that the difference between the average fuel economy of all domestic mid-size cars and all import mid-size cars is between -9.406 and -0.656.

4) We are 99% confident that the difference between the average fuel economy of all domestic mid-size cars and all import mid-size cars is between -9.406 and -0.656.

5) We do not know the population means so we do not have enough information to make an interpretation.

**Question 11**

Automobile manufacturers are interested in the difference in reaction times for drivers reacting to traditional incandescent lights and to LED lights. A sample of 26 drivers are told to press a button as soon as they see a light flash in front of them and the reaction time was measured in milliseconds. Each driver was shown each type of light. The average difference between the two reaction times (traditional – LED) was 51.126 ms with a standard deviation of 14.84 ms. If they wanted to calculate a 90% confidence interval for the difference in the average reaction time to the two types of light for all drivers, what is the margin of error?

1) 4.964

2) 3.827

3) 4.7875

4) 4.9713

5) 2.9104

**Question 12**

Researchers in the corporate office of an airline wonder if there is a significant difference between the cost of a flight on Priceline.com vs. the cost of the same flight on the airline’s own website. A random sample of 7 flights were tracked on Priceline.com and the airline’s website and the mean difference in price (Priceline.com – Airline Site) was $-96.678 with a standard deviation of $11.8541. Create a 99% confidence interval for the true average difference in costs between the vendors.

1) (-100.3854, -92.9706)

2) (-113.2889, -80.0671)

3) (-112.3572, -80.9988)

4) (-101.1584, -92.1976)

5) (113.2889, -80.0671)

**Question 13**

A new drug to treat high cholesterol is being tested by pharmaceutical company. The cholesterol levels for 27 patients were recorded before administering the drug and after. The 99% confidence interval for the true mean difference in total cholesterol levels (after – before) was (-78.82, -31.18). Which of the following is the appropriate conclusion?

1) We are 99% confident that the average difference in cholesterol levels is positive, with the higher cholesterol levels being before the drug regimen.

2) There is not a significant difference in average cholesterol levels before and after the drug.

3) We are 99% confident that the average difference in cholesterol levels is negative, with the higher cholesterol levels being after the drug regimen.

4) We are 99% confident that the average difference in cholesterol levels is negative, with the higher cholesterol levels being before the drug regimen.

5) We are 99% confident that the average difference in cholesterol levels is positive, with the higher cholesterol levels being after the drug regimen.

**Question 14**

Automobile manufacturers are interested in the difference in reaction times for drivers reacting to traditional incandescent lights and to LED lights. A sample of 13 drivers are told to press a button as soon as they see a light flash in front of them and the reaction time was measured in milliseconds. Each driver was shown each type of light. The average difference in reaction times (traditional – LED) is 3.5 ms with a standard deviation of 6.49 ms. A 95% confidence interval for the average difference between the two reaction times was (-0.42, 7.42). Which of the following is the best interpretation?

1) We are 95% confident that the average difference in the reaction times of the drivers sampled is between -0.42 and 7.42.

2) We are certain the average difference in reaction times between the two light types for all drivers is between -0.42 and 7.42.

3) The proportion of all drivers that had a difference in reaction times between the two lights is 95%.

4) We are 95% confident that the difference between the average reaction time for LED lights and the average reaction time for traditional lights is between -0.42 and 7.42.

5) We are 95% confident that the average difference in reaction time between the two light types for all drivers is between -0.42 and 7.42.

**Attempt Score:14** / 14

**Overall Grade** (average of all attempts)**:14**/ 14

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