MATHEMATICS

TAT 3001 Practice Exam

 

 

 

 

 

 

Please take the time to review the following mathematical problems. If you have are able to solve these problems you will be in GOOD shape for your final exam.. You may check your solutions at the end of this document.

 

Remember you only have ONE attempt at the final exam MAKE IT COUNT!

 

Your exam is open note and open book please take advantage of the opportunity to use these resources

 

 

 

1. An admissions advisor for a local college decides he would like to determine the average age of students at the college for some promotional materials. To do this he pulls the records of 200 random students at the college.

What type of study is this (observation or experiment), what is the variable of interest?

 

2. Fifty registered nurses are asked how many hours they work each week. Based on this sample the estimated average is 46 hours with a margin of error of 4.9 hours. Use the given values to identify the confidence interval likely to contain the actual population mean.

 

3. The following histogram represents the movie lengths hit movies in 1998

 

 

 

 

 

a How many movies total are represented in this histogram?

 

b. How many movies lasted less than 150 minutes?

 

c. How many movies lasted more than 150 minutes?

 

d. What is the highest possible movie length represented in this histogram?

 

4. A real estate agent records the price of the eight homes she has listed at this moment they are as follows:

123,000 155,000 139,000 140,000 159,000 34,000 121,000 and

434,000

a. Find the mean and median of the data presented

b. Identify the outlier on the LOW end of the data set, remove this value and calculate the new mean and median

c. Identify the outlier on the HIGH end of the data set, remove this value what is the new mean and median of the data set (HINT be sure you put your low value back in!)

5. In a survey of 2,150 US teachers it was found that 60% of them said if they could start their careers again they would choose a different career. The margin of error was 5 percentage points

What was the goal of this study

What is the population

Identify the population parameter of interest

Identify the sample

What is the raw data collected for this study

Identify the sample statistic

Based on the margin of error identify the range of values likely to contain the population parameter of interest

6. The following table shows the average weight and standard deviation for different colored M and M’s in grams

Color Mean Standard deviation
Red 0.91 0.03
Yellow 0.92 0.03
Blue 0.90 0.02

Assume the machine filling the bag is set to reject M and M’s more than 2 standard deviations above and below the mean

For each color find the range of weights that are acceptable to the vending machine

Red:

Yellow:

Blue:

 

7. The following table measures the weight of M and M’s (in grams) of various colors of the candy.

Orange Blue Green

0.903 0.838 0.911

0.92 0.875 1.002

0.861 0.87 0.902

1.009 0.956 0.93

0.971 0.968 0.949

0.898 0.89

0.942 0.902

0.897

 

Use a 0.01 level of significance to test the claim that the different colors all have the same mean.

a. Find the p value

b. At this level is there significant evidence to say that all colors have the same mean?

8. A statistics student decided to roll a dice 50 times, she rolled the number two 11 times. Is the difference between what the student rolled and what is theoretically expected statistically significant?

9. Data was recorded for the number of home runs hit for three baseball players, Mark McGwire, Sammy Sosa and Barry Bonds. The Analysis of Variance results obtained from software are found below. The significance level is 0.10 in testing the null hypothesis.

Source: DF: SS: MS: Test Stat Critical F: P-Value:

Treatment: 2 9546.87 4773.43 3.35 2.32 0.036

Error: 206 293224.08 1423.41

Total: 208 302770.95

 

What is the null hypothesis?

What is the alternative hypothesis

What is the p value

Is there sufficient evidence to support the claim that the three players have different average number of home runs hit?

 

10. A researcher wishes to estimate the average number of hours that high school students spend on facebook each day. A margin of error of 0.22 hours is desired. Past studies suggest a population standard deviation of 2.1 hours is reasonable, estimate the minimum sample size needed to estimate the population mean with the desired accuracy.

 

11. A study was done among 1200 Walden Students. Among these students 700 were Masters of Nursing students and 520 of these were taking their first online course. Among the 500 other students, 410 were taking their first online course.

a. What percentage of students were nursing students

b. What percentage of nursing students were taking their first online course

c. Among those who were NOT nursing students what percentage were taking their first online course?

d. What percentage of the students were taking the first online course?

12. On research study of illegal drug use among teenagers shows a decrease from 11.4% in 1997 to 9.5% now. Suppose a study in a large high school reveals that in a simple random sample of 1054 students 97 report using illegal drugs. Use the 0.05 significance level to test the principal’s claim that illegal drug use is below the national average.

a. formulate the null and alternative hypothesis

b. The sample statistics are the sample size n=1054 and the sample proportion , find the sample proportion rounded to four decimal places

c. Find the standard score, z for the sample proportion

d. Is there sufficient evidence to support the principals claim that the illegal drug use at this school is below the national average?

13. Suppose you know the distribution of sample proportions in samples of 300 registered voters who will vote for candidate A is normal with a mean of 0.34 with a standard deviation of 0.02. Suppose you select a random sample of 300 voters and find the proportion of those willing to vote for candidate A is 0.38.

a. How many standard deviations is the sample proportion from the mean of the distribution of sample proportions?

b. What is the probability the selected sample would have a proportion of less than 0.38?

14. You select a random sample of n=15 families in your neighborhood and find the following family sizes.

7
8
11
10
9
7
8
8

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