# Hypothesis Testing, Confidence Interval, Graphs

NOTE: Please ensure that when applicable all computations are clearly provided to indicate how you arrived at your final response. Failure to do so will result in a loss of half the allotted marks for the problem in question.

1. Identify each of the following statistics as either descriptive or inferential:

a). Seventy-three percent of Italian-American households in the U.S. own a computer.

b). Households with children under the age of 18 are more likely to have access to the Internet(62 percent) than family households with no children (53 percent).

c). Hank Aaron hit 755 career home runs.

d). The average SAT score of incoming college freshmen at a local college was 950.

e). On a recent poll, 67 percent of Americans had a favourable opinion of the President of the United States.

2. Classify the following data as nominal, ordinal, interval, or ratio.

Explain your choice.

1. Average monthly temperature in degrees Fahrenheit for the city of Wilmington throughout the year.

2. Average monthly rainfall in inches for the city of Wilmington throughout the year.

3. Performance rating of employees classified as Above Expectations, Meets Expectations, or Below Expectations.

4. Education level of survey respondents:

a. Level Number of respondents

b. High School 168

c. Bachelor's degree 784

d. Master's degree 212

5. Marital status of survey respondents:

a. Status Number of respondents

b. Single 28

c. Married 189

d. Divorced 62

6. Age of the respondents.

7. Gender of the respondents.

8. The year in which the respondents were born.

9. The voting intentions of the respondents in the survey classified as Republican, Democrat, or Unclassified.

3. The following table represents the exam grades from 36 students from a certain class I might have taught.

Exam Scores:

60 95 75 84 85 74

81 99 89 58 66 98

99 82 62 86 85 99

79 88 98 72 72 72

75 91 86 81 96 86

78 79 83 85 92 68

a). Construct a Frequency distribution with 9 classes ranging from 56 to 100 from the data above.

b). Construct a relative and cumulative frequency distribution from the data in Problem # 3 above

c). Construct a stem and leaf diagram from the data in Problem # 3 above using one stem for the scores in 50s, 60s, 70s, 80s, and 90s.

4. Calculate the variance, standard deviation and range for the following population data set:

84, 82, 90, 77, 75, 77, 82, 86, 82.

5. A company counted the number of their employees in each of the age classes as follows. According to this distribution, what is the standard deviation for the age of the employees in the company?

Age Range Number of employees

20-24 8

25-29 37

30-34 25

35-39 48

40-44 27

45-49 10

6. A data set that follows a bell-shape and symmetrical distribution has a mean equal to 75 and a standard deviation equal to 10. What range of values centered around the mean would represent 95 percent of the data points?

7. You are asked to gather a systematic sample from the local phone book with 75,000 names. If every kth name in the phone book is to be selected, what value of k would you choose to gather a sample size of 500?

8. Consider a population that is defined as every employee in a particular company. How could you use stratified sampling to gather a sample to participate in a survey involving employee satisfaction?

9. The following are grade point averages for 15 randomly selected college students:

2.3 3.3 2.6 1.8 0.2 3.1 4.0 0.7

2.3 2.0 3.1 1.4 1.3 1.6 1.6

For the data set above assume the population is normally distributed and find:

a) The sample mean

b) The sample standard deviation

c) Construct a 99% confidence interval for the population mean μ

10. A computer company wants to estimate the mean number of hours per week all adults use computers at home. In a random sample of 21 adults, the mean length of time a computer was used at home was 5.3 hours. From past studies, the computer company assumes σ is 0.9 hour and that the population is normally distributed. Use this information to construct the 90% and 99% confidence intervals for the population mean. Which interval is wider?

(3 points)

11. For the example given below, assume each sample is taken from a normally distributed population and construct the confidence intervals for:

CD Players: A magazine includes a report on the prices of compact disc players. The article states that 26 randomly selected CD players had a standard deviation of $150. Use a 95% confidence interval.

a). the population variation σ²

b). the population standard deviation σ

12. Translate the newspaper excerpt below into a confidence interval for p

In a survey of 1001 adults 27% said they had smoked a cigarette in the past week. The survey's margin of error is plus or minus 3%.

13. Stating the hypotheses:

In the following examples :

a. State the claim mathematically.

b. Write the null and alternative hypothesis mathematically.

c. Identify which is the claim.

Shipping errors: As stated by a company's shipping department, the number of shipping errors per million shipments has a standard deviation that is less than 3.

What Shoppers buy: A research organization reports that 9% of all adult grocery shoppers in the U.S. never buy the store brand.

Survival Times: A study claims that the mean survival time for certain cancer patients treated immediately with chemotherapy and radiation is 24 months.

14. Testing Claims:

For the data provided below:

Government inefficient and wasteful: A government watchdog association claims that 70% of people in the U.S. agree that the government is inefficient and wasteful. You are asked to test this claim. You find that in a random sample of 1165 people in U.S., 746 agreed with this view. At α=0.05, do you have enough evidence to reject the associations claims?

a. Write the claim mathematically AND identify null and alternative hypotheses

b. Find the critical values AND identify the rejection regions.

c. Find the standardized test statistic

d. Decide whether to reject or fail to reject the null hypothesis

e. Interpret the decision in the context of the original claim.

15. Test the claim that the proportion of Independent voters in a particular city is less than 40%. A random sample of 175 voters was selected and found to consist of 30% Independent voters. Use α=0.01 and determine the p-value for this sample.

16. In your textbook 'Elementary statistics: picturing the world' complete the following problems:

a). Chapter 9; Exercise 9.2; ( p. 462):

Complete Problem Nos. 1-8 : Match the description in the left column with a description in the right column.

b). Chapter 9; Exercise 9.3; - Finding types of variations and the coefficient of determination.

Complete Problem Nos. 11 and 12. (p.475)

https://brainmass.com/statistics/confidence-interval/hypothesis-testing-confidence-interval-graphs-351936

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis, confidence interval, descriptive statistics, standard error of estimate and coefficient of determination. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

Frequcny distribution chart and confidence interval

Scenario:

You are an associate assigned to the claims department of a major insurance company. A policy holder has had an accident with his classic 1968 Oldsmobile Cutlass Supreme.

At issue is the consideration of his brakes. Recently, he was driving down the road and was apparently unable to stop in time when a woman driving a 2004 Porsche Boxster "S" pulled out in front of him; subsequently, he "T-boned" the Porsche. Injured in the accident were the, driver of the Porsche, who was 7 months pregnant with twins and her elderly mother-in-law who has cerebral palsy; both of which were from out of town. Now with their only means of transportation "totaled" they are stranded.

The Porsche driver's insurance company, which is USA, contends that your policy holder is at fault because his car was not up to current standards. There seems to be a difference in the braking distance between vintage brake shoes and current ones.

Your policy holder is a self proclaimed, "shade tree" mechanic and a classic car enthusiast. As a matter of fact, he once owned a rather successful auto mechanic business and is now the President of the State of Florida Oldsmobile Club which has a substantial lobby in Tallahassee.

Your boss decided that because you are enrolled in a statistics class you should be pressed into service to assist and, as such, you have questioned the policy holder extensively. From your investigation you discover that he does his own work and recently replaced his brakes with a vintage brand of asbestos brake shoes. The contention is that modern brake shoes stop a vehicle which is traveling at 35 mph (which your policy holder was pr oven to be doing) at 20.5 feet, give or take one foot either side.

Your company's research department gathered the following in support:

Out of 42 sets available, worldwide, of vintage asbestos brake shoes, 20 were selected for testing. Below are the results:

23.2 18.1 19.2 20.3 23.0

26.0 24.6 16.9 17.3 23.4

28.6 17.2 23.2 18.7 19.6

20.8 24.2 25.0 19.8 17.6

Questions;

A. What is the percentage of these pads that fall within the current and

more modem parameters?

B. Arrange this data in class intervals and construct a Frequency

Distribution chart.

C. Construct a confidence interval to predict the boundaries of this

parameter.

D. Your policy holder actually contends that the vintage brake shoes exceed the modem standards. Is there evidence that would suggest he is correct?

E. Assuming that the stopping distance between the vintage brake shoe and the modem equivalent is the same, what is the probability that either one tested will stop a vehicle of this size or larger, within 5 feet of the true mean?

F. What is the probability that the difference between the stopping. distance with the vintage brake pads and the stopping distance of the newer style brake pads being as large as reported or larger if there is no difference in the true stopping distance averages between the two styles?