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)

 

1. The study of statistics can be separated into two areas: __________________ statistics and ____________________ statistics.

 

2. 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.

 

3. Three measures of central location are ________, ____________, and __________.

 

4. The __________ value separates the region where the null hypothesis is rejected from the region where it is not rejected.

 

5. 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)

 

6. A cumulative frequency polygon is created by line segments connecting the class _______ and the corresponding cumulative frequencies.

 

7. 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.

 

8. A ____________ is a graphical display based on five statistics: the maximum and minimum values, the first and third quartiles, and the median.

 

9. What is the probability of a z value between -0.76 and 1.43? _________

 

10. 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)

 

11. Inferential statistics helps researchers make generalizations about large populations by using data from a sample of a population. (T/F)

 

12. Histograms are usually used to represent categorical variable. (T/F)

 

13. The data value that represents the 1^st quartile is less than the data value that represents the 3^rd (T/F)

 

14. If a population follows the normal distribution, the shape of the distribution of sample means is left skewed. (T/F)

 

15. 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)

 

16. is often used to estimate the ___________ of a population.

 

1. Median    b) Mean      c) Mode       d) Standard Deviation       e) Variance

 

17. 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?

 

191. 469            b)  272          c)  563           d)   4              e)  19

 

18. 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. (38.3%, 52.9%) b) (39.5%, 51.8%)      c)  (40.5%, 50.8%)        d) (37.6%, 53.7%)

 

19. 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. (25.5, 28.5)     b) (26.3, 28.5)    c) (26.3, 27.2)   d) (26.8, 27.2)   e) (61.7, 66.3)

 

20. 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 . . .

 

1. 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

 

1. For the distribution: 7, 12, 10, 12, 4, 13, 5, 17, 10. Find                         (20 points)

 

1. Mode = b) range =

 

1. Median = d) The  sample mean,  =

 

1. 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

 

 

1. Sample variance, =

 

1. The sample standard deviation,

 

 

2. 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.

 

3. 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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4. 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?

 

 

 

 

 

 

 

5. 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.