**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 1
^{st}quartile is less than the data value that represents the 3^{rd}(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 universityâ€™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.