The exam covers information from Chapters 1-9. Point values are associated with the questions. Make sure to answer all elements of each question directly. You are welcome to use Excel, SAS, or hand calculate answers. You can either (1) type and upload all answers (you are welcome to type within this word document) or (2) bring a printed copy to my office (St. Joe's G-7 - you can slide under my door or in the secretary’s office if I am not in – as long as the copy is there Monday morning, it will be considered on time).
Please turn in and show all work!
I understand mathematical mistakes happen and I can still award partial credit if all work is done correctly and I can follow your procedures.Good luck!
1. (10 points). An athletics trainer wants to measure the effectiveness of his training skills with a population of 63 athletes. He selects athletes by waiting at the training facility and pulling aside every third athlete to give him or her a questionnaire.
1a. Is this sample design an example of random sampling? Explain.
Yes, because it is every third athlete. They all have an equal chance of beingchosen.
1b. Assuming that all students attend his class that day, how many students will he select to complete the questionnaire?
He will choose 21. 63/3 = 21.
1c. A specific question on the questionnaire asks about verbal coaching effectiveness on a0-10 scale (0 = extremely confusing to 10 = extremely clear) with the following scores:
0, 9, 8, 8, 5, 4, 3, 2, 6, 5, 8, 1, 4, 10, 5, 8, 6, 7, 5, 4, 9
Calculate the mean, median, and mode of these scores.Which is the best measurement to report verbal coaching effectiveness?Why?
Mean – 117/21 = 5.57
Median –0, 1, 2, 3, 4, 4,4, 5, 5, 5, 5, 6, 6, 7, 8,8, 8, 8, 9, 9, 10= 5
Mode – The numbers that appear most often are 5 & 8. This number set is bimodal.
I think that the median would be the most accurate because it is not positively or negatively skewed.
1d. Calculate the variance and standard deviation of the sample. What conclusions about verbal coaching effectiveness can you make with this added information?
Variance – 7.45
Standard Deviation –2.73
ss – 149. 14
s2 = s/(n - 1) = 149.14/(21 - 1) = 7.46
s =Ös2 =Ö7.46 =2.73
1e. The trainer decided to change his method after the initial sample and then re-sampled his athletes (same sample method) to see if there was an improvement in his verbal coaching effectiveness score. The new average verbal coaching effectiveness score is 7.2 with a standard deviation of2.2. What is the probability that a sample mean selected from this population wouldshow no change (0) or a negative change (less than 0) after the new lectures were implemented?
2. (10 points). A national measure of religiosity is measured for all undergraduate students who attend private religious based universities in the United States. The scores are approximately normally distributed with amean of 80and a standarddeviation of 18.1. Seton Hill University measured an incoming freshman class (300 students) to identify if the religiosity of SHU students is significantly different from that of the entire private religious based university undergraduate student population. In the SHU freshman class a sample mean of 84 was obtained (M= 84). Assume normal distribution and test at a 0.05 level of significance (a= .05).
2a. State the null and alternative (research) hypotheses.
2b. What type test is this? State the testing criteria.
2c. Compute the test statistic for this research.
2d. State whether to reject or retain the null hypothesis and interpret the result.
2e. What is the p-value associated with the test statistic?
2f. What summary conclusion can you make about SHU students compared to the overall private/religious affiliated student population?
3. (10 points). A sample of final exam scores is normally distributed with a mean equal to 77 and a variance equal to 12.
3a. What percentage of scores are between 70 and 80?
3b. What raw score is the cutoff for the top 10% of scores?
3c. What is the probability of a score less than 70?
3d. What is the probability of a score higher than 90?
4. (10 points). A local zoo wants to compare day versus evening visiting times to determine when is a more popular time for their polar bear exhibit. They randomly observed people viewing the exhibit and noted 30 visitors stayed for an average of 15 minutes with a standard deviation of 3.1 during the day. During the evening, 26 visitors stayed for an average of 9 minutes with a standard deviation of 2.0. Assuming a normal distribution, determine if there is a significant difference in viewing time between day and evening hours.
4a. Which test will you use to determine significance?
4b. State the null and alternative hypotheses
4c. State your research criteria
4d. Calculate your test statistic
4e. State your decision regarding significance and interpret your results.
4f. Calculate the confidence interval, if applicable.
4g. Calculate the effect size and proportion of variance, if applicable
5. (5 points). A professor records the time (in minutes) that it takes 16 students to complete an exam. Below is the data in minutes:
23, 25, 43, 48, 32, 14, 21, 38, 44, 29, 39, 50, 20, 41, 33, 40
5a. What is the Sum of Squares (SS)?
5b. What is the variance?
5c. What is the standard deviation?
5d. What type of concluding statements can you make about this group of students regarding time to complete exams?
6. (5 points). The 9th grade at a small, private school (N = 25 students) completed a math aptitude test. The school is interested in using the test scores for placement into different math courses. Below are the scores, based on a 100 point scale:
91, 64, 72, 80, 85, 99, 60, 83, 74, 100, 55, 82, 86, 91, 74, 87, 77, 63, 93, 88, 77, 85, 94, 71, 65
6a. What would be the best way to group this data for frequency purposes? Why?
6b. Provide your frequency chart for the data.
6c. Would relative frequency or cumulative relative frequency be useful to use in this situation? Why or why not?
6d. Provide a histogram representation of your data set.
6e. Describe your histogram. Does it reflect a normal distribution? Explain.
7. (10 points). The average income in the United States is $56,516. A team of researchers is interested to see the impact of geographical location on income. A sample of 35 participants from the northeastern region of the United States were asked to provide their income. The average income was $49,520 with a standard deviation of $1,200.
7a. Which test will you use to determine significance? One tail or two tail?
7b. State the null and alternative hypotheses
7c. State your research criteria
7d. Calculate your test statistic
7e. State your decision regarding significance
7f. Calculate the confidence interval, if applicable.
7g. Calculate the effect size and proportion of variance, if applicable.
8. (15 points). A high school principal is looking to examine if there is a significant difference in absences between freshman and seniors at his school. He randomly samples 10 freshman and 10 seniors and records their number of absences:
Freshman
|
Seniors
|
1
|
5
|
2
|
4
|
4
|
3
|
3
|
3
|
0
|
2
|
1
|
0
|
2
|
5
|
3
|
2
|
5
|
6
|
1
|
1
|
8a. Which test will you use to determine significance?
8b. State the null and alternative hypotheses
8c. State your research criteria
8d. Calculate your test statistic
8e. State your decision regarding significance
8f. Calculate the confidence interval, if applicable.
8g. Calculate the effect size and proportion of variance, if applicable.
9. (15 points). Americans tend to eat out (commercially prepared meals) approximately 4.2 times per week. A researcher feels his community might be different than the national average. He examines a random sample of 15 families and recorded how often they ate out per week:
1, 0, 7, 5, 3, 2, 3, 1, 4, 3, 4, 2, 6, 2, 4
Assuming a normal distribution, determine if there is a significant difference between this community compared to general Americans.
9a. Which test will you use to determine significance? One tail or two tail?
9b. State the null and alternative hypotheses
9c. State your research criteria
9d. Calculate your test statistic
9e. State your decision regarding significance
9f. Calculate the confidence interval, if applicable.
9g. Calculate the effect size and proportion of variance, if applicable.
10. (10 points). A study conducted by the Center for Disease Control (CDC) found that the average American exercises vigorously for an average of 17 minutes per day, with a standard deviation of 1.2.A researcher who works with teenagers with health issues wants to determine if the group is different than the national average. The researcher finds that his group of 25 teens exercises 15 minutes per day. Assume normal distribution and test at a 0.05 level of significance (a= .05).
10a. State the null and alternative (research) hypotheses.
10b. What type test is this? State the testing criteria.
10c. Compute the test statistic for this research.
10d. State whether to reject or retain the null hypothesis and interpret the result.
10e. What is the p-value associated with the test statistic?
10f. What summary conclusion can you make about the teen population compared to the average American?