INTRODUCTION TO STATISTICS (MATO 205)
Hampton University, University College
FINAL EXAM
Name__________________________________ Date__________________
Instructions: You are required to work the questions independently. Do not seek help from
anyone. Follow Hampton University Code of Conduct.
Fill in the Blank. (1 point each)
- The study of statistics can be separated into two areas: __________________ statistics and ____________________ statistics.
- The ____________ is the probability of finding a value of the test statistic at least as extreme as the one observed, given that the null hypothesis is true.
- Three measures of central location are ________, ____________, and __________.
- The __________ value separates the region where the null hypothesis is rejected from the region where it is not rejected.
- As the degrees of freedom increase, the t distribution _________ . (approaches the binomial distribution, exceeds the normal distribution, approaches the z distribution, becomes more positively skewed)
- A cumulative frequency polygon is created by line segments connecting the class _______ and the corresponding cumulative frequencies.
- The ________________ states that for any symmetrical, bell-shaped frequency distribution, approximately 95% of the observations will lie within plus or minus two standard deviations of the mean.
- A ____________ is a graphical display based on five statistics: the maximum and minimum values, the first and third quartiles, and the median.
- What is the probability of a z value between -0.76 and 1.43? _________
- In a ________ -tailed test, the significant level is divided equally between the two tails. (one, two, neither)
Decide whether each statement is true or false. (1 point each)
- Inferential statistics helps researchers make generalizations about large populations by using data from a sample of a population. (T/F)
- Histograms are usually used to represent categorical variable. (T/F)
- The data value that represents the 1st quartile is less than the data value that represents the 3rd (T/F)
- If a population follows the normal distribution, the shape of the distribution of sample means is left skewed. (T/F)
- The median is more resistant measure of central tendency than the mean. (T/F)
Circle the best answer for each of the following: (1 point each)
- is often used to estimate the ___________ of a population.
- Median b) Mean c) Mode d) Standard Deviation e) Variance
- A university’s administrator proposes to do analysis of the proportion of graduates who have not found employment in their major field one year after graduation. In previous years, the percentage averaged 13%. He wants the margin of error to be within 0.04 at a 99% confidence level. What sample size will suffice?
- 469 b) 272 c) 563 d) 4 e) 19
- When 252 college students are randomly selected and surveyed, it is found that 115 own a car. Construct a 99% confidence interval for the percentage of all college students who own a car.?
- (38.3%, 52.9%) b) (39.5%, 51.8%) c) (40.5%, 50.8%) d) (37.6%, 53.7%)
- A sample of 64 statistics students at a small college had a mean mathematics ACT score of 27 with a standard deviation of 6. Find a 95% confidence interval for the mean mathematics ACT score for all statistics students at this college.
- (25.5, 28.5) b) (26.3, 28.5) c) (26.3, 27.2) d) (26.8, 27.2) e) (61.7, 66.3)
- When we estimate the standard deviation from a sampling distribution using statistics found from the data because the true parameters were not given, the estimate is called . . .
- Point estimate b) extrapolating c) standard error d) z-score e) guess estimate
Free Response Section
You Must Show Your Work to Earn Full Credit
- For the distribution: 7, 12, 10, 12, 4, 13, 5, 17, 10. Find (20 points)
- Mode = b) range =
- Median = d) The sample mean, =
- Use the table below to find the sample variance,
| Data Value, | Mean Deviation, | Mean Deviation Squared, |
| 7 | ||
| 12 | ||
| 10 | ||
| 12 | ||
| 4 | ||
| 13 | ||
| 5 | ||
| 17 | ||
| 10 | ||
- Sample variance, =
- The sample standard deviation,
- The Philadelphia Regional Transport Authority wishes to estimate the proportion of central city workers that use public transportation to get to work. A recent study reported that of 100 workers, 64 used public transportation. (15 points)
- Estimate the value of the population proportion.
- Develop a 90% confidence interval for the population proportion.
- Interpret your interval.
- What are the minimum, first quartile, median, third quartile, maximum, interquartile range, and range of the data set below? Make a box-and- whisker plot. (15 points)
25, 25, 30, 35, 45, 45, 50, 55, 60, 60
- The cost of weddings in the United States has skyrocketed in recent years. As a result, many couples are opting to have their weddings in the Caribbean. A Caribbean vacation resort recently advertised in Bride Magazine that the cost of a Caribbean wedding was less than $10,000. Listed below is a total cost for a sample of eight Caribbean weddings.
$9,700 $9,400 $11,700 $9,000 $9,100 $10,500 $ 9,100 $9,800
At the 0.05 significance level, is it reasonable to conclude the mean wedding cost is less than $10,000 as advertised? (15 points)
- State the null and alternate hypothesis.
- How many degrees of freedom are there?
- Give the decision rule
- Compute the value of . What is your decision regarding the null hypothesis?
- A recent article in USA Today reported that a job awaits 33% of new college graduates. The major reasons given were an overabundance of college graduates and a weak economy. A survey of 200 recent graduates from your school revealed that 80 students had jobs. At a 99% level of confidence, can we conclude that a larger proportion of students at your school have jobs? (15 points)
- State the null and alternate hypothesis.
- Determine which distribution to use for the test statistic, and state the level of significance.
- Calculate the necessary sample test statistics
- Draw a conclusion and interpret the decision.
