MTH540 – Introduction to Elementary Statistics
Biowizard901. 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%) than family households with no children (53 %).
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% of Americans had a favorable opinion of the transportation services provided by their local authorities.
2. Classify the following data as nominal, ordinal, interval, or ratio.
Explain your choice.
- Average monthly temperature in degrees Fahrenheit for the city of Wilmington throughout the year.
- Average monthly rainfall in inches for the city of Wilmington throughout the year.
- Performance rating of employees classified as Above Expectations, Meets Expectations, or Below Expectations.
- Education level of survey respondents:
Level
- High School
- Bachelor’s degree
- Master’s degree
- Marital status of survey respondents:
Status
- Single
- Married
- Divorced
- Age of the respondents.
- Gender of the respondents.
- The year in which the respondents were born.
- 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 above
c). Construct a stem and leaf diagram from the data 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 representative 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?
11. For the example given below, assume the sample is taken from a normally distributed population and construct the indicated confidence interval for:
a). the population variation σ²
b). the population standard deviation σ
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.
12. 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.
13. Testing the Claim:
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.
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