Confidence Interval Worksheet with Sample Data MTH 160: Statistics

Read the following scenario and complete each of the problems below:

A flashlight company claims that the new bulb in its heavy-duty flashlight will average 246 hours of light. A statistics student decides that he/she wants to test this claim at a 5% level of significance to determine if there is evidence to support the claim. The student randomly selects and tests 15 flashlight bulbs and records how long the bulb lasts until it burns out. Assume the life of a bulb is normally distributed. T

he data is in the table below

Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Hrs: 246 224 231 242 237 240 243 236 239 255 256 239 247 231 253

A. The standard deviation of the population is 7.4 hours. Construct a 95% confidence interval for this study.

B. Same scenario, but the population’s standard deviation is not known. Construct a 95% confidence interval for this study.

C. Write a statement comparing and contrasting the two confidence intervals and results.

Read the following scenario and complete each of the problems below:

A new car manufacturing company has emerged and has claimed that its new hybrid car, the Pusho, gets a better gas mileage than the highest ranked Toyota Prius. Consumer Reports Magazine decides to test this claim at a 5% level of significance. Consumer Reports randomly selects 10 of each type of car, calculates the miles per gallon for each car in the study, and records the data in the table below. Assume miles per gallon of the cars is normally distributed.

Pusho 54.1 52.4 55.7 49.7 50.6 48.9 51.8 54.5 56.9 49.8

Prius 53.2 54.3 49.8 50.1 50.5 56.1 47.8 53.4 56.8 48.7

A. Construct a 90% confidence interval for the difference in the gas mileage of Pusho and Prius.

B. Construct a 95% confidence interval for the difference in the gas mileage of Pusho and Prius.

C. Write a statement comparing and contrasting the two confidence intervals and the significance of having 0 in both of those intervals.

A statistical program is recommended.

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:

y = β₀ + β₁x + ε

where

• y = traffic flow in vehicles per hour
• x = vehicle speed in miles per hour.

The following data were collected during rush hour for six highways leading out of the city.

Develop an estimated regression equation for the data of the form

ŷ = b₀ + b₁x + b₂x².

(Round b₀ to the nearest integer and b₁ to two decimal places and b₂ to three decimal places.)

ŷ =

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.) vehicles per hou

question 2-

A statistical program is recommended.

Car manufacturers produced a variety of classic cars that continue to increase in value. Suppose the following data is based upon the Martin Rating System for Collectible Cars, and shows the rarity rating (1–20) and the high price ($1,000) for 15 classic cars.

Develop an estimated multiple regression equation with x = rarity rating and

x²

as the two independent variables. (Round b₀ and b₁ to the nearest integer and b₂ to one decimal place.)

ŷ =

Consider the nonlinear relationship shown by equation (16.7):

E(y) = β₀β₁^x

Use logarithms to develop an estimated regression equation for this model. (Round b₀ to three decimal places and b₁ to four decimal places.)

log(ŷ) =

ACC 3010 Project 3 Part 1

The patient is a 38 year old male plant manager and new long distance runner presenting with complaints of left anterolateral hip and thigh pain. He was referred to physiotherapy from his orthopedist, who diagnosed him with greater trochanteric bursitis.
His onset of symptoms was 6 weeks prior to the initial evaluation, after running a marathon (26.2 miles). By the end of the race, he was in intense, constant pain, rated at a 5/10 that remained constant for 3 days after. His symptoms became intermittent, and have not changed much since that time. His plan was to run 4 marathons in the next year, but he has stopped running completely, as every time he runs the pain comes back to the same intensity it was immediately after the race.
Since becoming symptomatic he has tried many stretches and strengthening exercises he researched on the internet. He has also received advice from his massage therapist. However, the same pain comes back when he runs. He has good shoes, and changes them every 250-300 miles, per industry recommendations. Because of all of his research, he is concerned that this is an issue that is going to keep him from running altogether.
When asked if the patient had any imaging, he replied “only an xray”. Then he said, “Why, do you think I need an MRI?” Sensing fear of life-altering structural damage, the patient was assured that one of the goals of physiotherapy is to determine the right place for them. With a careful assessment over 2-3 visits, we should know if further testing is necessary.


1. Given the history, anatomy and function of the hip, which structures are you going to examine? Explain why and how you will perform the examination of these structures.
2. What functional activities would you assess and how would you establish these    functional baselines. How vigorous can you be in your examination?
3. What examination tests would you use, and why would you use them?
4. What other subjective information would you get from this runner?

13. A manager wants to know whether customers in Taiwan, on average, would spend more than $2,000 per month on the service that is similar to what her company provides. The following information regarding the consumer behavior of 49 customers was provided by the marketing research team: sample mean = $2,400 and sample standard deviation = $1,800. Using the sample information provided and 0.05 significance level, determine the critical value and calculate the value of the test statistic.

A. Critical value = –1.96 & +1.96, and Test statistic = –1.56

B. Critical value = –1.645, and Test statistic = –1.56

C. Critical value = +1.645, and Test statistic = +1.56

D. Critical value = +1.96, and Test statistic = +1.56

14. Which of the following is NOT a characteristic of a normal variable?

A. It can be converted into the standard normal variable.

B. The values are from –∞ to +∞.

C. The center line is always at 0.

D. The probability of each individual value is virtually 0.

15. A tire manufacturer claims that his tires have a mean life of 60,000 miles when used under normal diving conditions. A firm that requires a larger number of these tires wants to test the claim. If the claim is correct, the firm will purchase the manufacturer’s tires; otherwise, the firm will seek another supplier. Now a random sample of 100 tires is taken and the mean and standard deviation of the 100 tires are found. Using these sample results, a 95% confidence interval for the mean life of the tire is estimated as from 56,789 to 63,211 miles. The manufacturer’s claim is tested at the 5% significance level. Based on the given information, what should the firm do?

A. The firm will seek another supplier.

B. Cannot be determined because of insufficient information.

C. The firm will purchase the manufacturer’s tires.

D. The firm will purchase half from the manufacturer and the other half from another supplier.

16. Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank’s Visa cardholders reveals that the amount is normally distributed with a mean of $1,735 and a standard deviation of $285. What interest payment is exceeded by only 15% of the bank’s Visa cardholders?

A. $1,438.60

B. $1,585.375

C. $1,884.625

D. $2,031.40

Acid Base titration Lab: Add NaOH to a hot sauce mixture, then to a ketchup mixture. ****The hot sauce mixture consisted of 20 mL DH20 AND 1.5g Hot sauce. Ketchup = 20 mL DH20 and 1.5 g ketchup. the below columns are the mLs added of NaOH, and the pH value at each point. 3rd column is derivative

A.) For each trial calculate mol NaOH needed to reach equiv. point, and the average concentration of C2H4O2 in each trial.

B.) What is the concentration of NaOH used (M) in each trial?

HOT SAUCE TRIAL-

mL pH derivative

0.00 3.50 0.49

0.5 3.76 0.44

1.0 3.98 0.37

1.5 4.13 0.31

2.0 4.27 0.26

2.5 4.39 0.24

3.0 4.50 0.23

3.5 4.62 0.23

3.75 4.68 0.22

4.0 4.73 0.21

4.25 4.78 0.21

4.5 4.83 0.22

4.75 4.89 0.23

5.0 4.95 0.23

5.25 5.01 0.24

5.5 5.07 0.26

5.75 5.13 0.28

6.0 5.21 0.31

6.25 5.29 0.33

6.5 5.37 0.37

6.75 5.47 0.44

7.0 5.58 0.54

7.25 5.72 0.73

7.5 5.93 1.13

7.75 6.20 2.00

8.0 6.70 3.59

8.25 8.05 4.84

8.5 9.60 4.25

8.75 10.38 2.75

9.0 10.83 1.59

9.25 11.09 0.90

9.5 11.27 0.55

10.0 11.49 0.39

10.5 11.64 0.30

11.0 11.75 0.24

KETCHUP TRIAL:

mL pH Derivative

0.0 3.95 0.50

0.5 4.21 0.49

1.0 4.45 0.48

1.5 4.68 0.47

2.0 4.91 0.49

2.25 5.04 0.56

2.5 5.19 0.66

2.75 5.36 0.85

3.0 5.59 1.26

3.25 5.89 2.12

3.5 6.45 3.57

3.75 7.85 4.28

4.0 9.01 3.42

4.25 9.61 2.22

4.5 9.98 1.42

4.75 10.26 0.96

5.0 10.47 0.67

5.5 10.75 0.52

6.0 10.94 0.44

Exercise 1: Stoichiometry and a Precipitation Reaction

Data Table 1. Stoichiometry Values.

Questions

A perfect percent yield would be 100%. Based on your results, describe your degree of accuracy and suggest possible sources of error.

The yield percentage of my experiment was a little over 91%. This means that approximately 9% was error, because maybe some of the precipitate didn’t filter through or some was still left in the beaker.

What impact would adding twice as much Na₂CO₃ than required for stoichiometric quantities have on the quantity of product produced?

There will be no impact because CaCl₂ is the limiting reagent. The product weight would still be the same.

Determine the quantity (g) of pure CaCl₂ in 7.5 g of CaCl₂•9H₂O.

Mass of CaCl₂•9H₂O is 273.12 g/mol

Mass of CaCl₂ is 110.98 g/mol

Moles of CaCl₂•9H₂O is 7.5g/273.12 g/mol= .0275 moles CaCl₂•9H₂O

So, .0275 moles• 110.98 g/mol= 3.05 g of CaCl₂

Determine the quantity (g) of pure MgSO₄ in 2.4 g of MgSO₄•7H₂O.

Mass of MgSO₄•7H₂O is 246.47 g/mol

Mass of MgSO₄ is 120.37

Moles of MgSO₄•7H₂O is 2.4g MgSO₄•7H₂O•120.37g MgSO₄/ 246.47g MgSO₄•7H₂O= 1.17 g MgSO₄

Conservation of mass was discussed in the background. Describe how conservation of mass (actual, not theoretical) could be checked in the experiment performed.

Conservation of the mass can be obtained by calculating the initial mass of the CaCl₂ and with that you can find the mass of the initial Ca and then find the mass of the final product. The mole ratio should already be known, so we can find the mass of Ca in the product and compare it with the initial mass of the Ca. which was used in the starting of the experiment.

LaRosa Machine Shop (LMS) is studying where to locate its tool bin facility on the shop floor. The locations of the five production stations appear in figure shown below.

In an attempt to be fair to the workers in each of the production stations, management has decided to try to find the position of the tool bin that would minimize the sum of the distances from the tool bin to the five production stations. We define the following decision variables:

X = horizontal location of the tool bin

Y = vertical location of the tool bin

We may measure the straight line distance from a station to the tool bin located at (X,Y) by using Euclidean (straight-line) distance. For example, the distance from fabrication located at the coordinates (1,4) to the tool bin located at the coordinates (X,Y) is given by .

CA8-10 WRITING (FIFO and LIFO) Harrisburg Company is considering changing its inventory valuation method from FIFO to LIFO because of the potential tax savings. However, management wishes to consider all of the effects on the company, including its reported performance, before making the final decision.

The inventory account, currently valued on the FIFO basis, consists of 1,000,000 units at $8 per unit on January 1, 2017. There are 1,000,000 shares of common stock outstanding as of January 1, 2017, and the cash balance is $400,000.

The company has made the following forecasts for the period 2017–2019.

Instructions

(a)   Prepare a schedule that illustrates and compares the following data for Harrisburg Company under the FIFO and the LIFO inventory method for 2017–2019. Assume the company would begin LIFO at the beginning of 2017.

(1)Year-end inventory balances.

(2)Annual net income after taxes.

(3)Earnings per share.

(4)Cash balance.

Assume all sales are collected in the year of sale and all purchases, operating expenses, and taxes are paid during the year incurred.

(b)   Using the data above, your answer to (a), and any additional issues you believe need to be considered, prepare a report that recommends whether or not Harrisburg Company should change to the LIFO inventory method. Support your conclusions with appropriate arguments.

Hello, I mainly need B answered. Thanks