Study Union(Taylor D.)

1. A UCF poll is being conducted to determine the percentage of students that believe they will graduate on time (4 years from their first semester). A random sample of 273 UCF students was taken.

Sample:

Population:

Inference:

Is the data collected a parameter or statistic? Why?

Qualitative or quantitative? Why?

2. Answer the following questions using the given sample:

9, 12, 8, 6, 9, 10, 27,

n: Mean: Median: Mode: Range:

Variance: Standard Deviation:

Is this data symmetric, left skewed, or right skewed?

How many observations fall within one deviation of the mean?

How many observations fall within two deviations of the mean?

Using this data, what would be the z score of 36? Given the data set, Is this value normal, a possible outlier, or a true outlier?

3. A normally distributed given data set has a mean of $1,500 with a standard deviation of $300. What proportion of observations are between $900 and $2,100?

Between $1,200 and $1,800?

More than $2,400?

NOW… assume the data set above is NOT normally distributed…*cough*cough*use Chebyshev’s Theorem*cough*cough*

4. Which score is better?

57 on first test (Assume pop. mean is 72 and std. 20)450 on second test (Assume pop. mean is 500 and std. 80)

5.

What is the probability, if someone were selected at random from anywhere in the country, they voted for Hillary Clinton?

What is the probability, if someone were selected at random from Washington DC, they voted for Hillary Clinton?

6.

P ( z > 0.11)

P (z < 0.11)

P(0 < z < 1.24)

P (z > zo) = .8944

7. Suppose you are to choose from a work team of 8 people from 15 available, how many ways can you arrange this team?

8. Lottery time! Pick 6 numbers from 53 total. How many combinations can be found?

9. 30% of households on the block watch Monday Night Football. 15 households were sampled.

- x is binomial with n = 15 and p = 0.3

What is the probability that x is less than 3?

What is the probability that x is equal to 3?

What is the probability that x is more than 3?

What is the expected value?

10. x is binomial with n = 10 p = .3

What is the probability that 6 or more people survive?

What is the probability that exactly 7 survive?

11. A factory crafts and manufactures milk cartons. Unfortunately, factory defects are inevitable. The probability of this factory producing a carton with a puncture is 0.05, while the probability of the factory smashing a carton is 0.08. The probability of the factory producing a carton that is punctured AND smashed is 0.004.

If randomly selected, what is the probability that a carton out of the assembly is punctured or smashed?

Are they mutually exclusive?

12. There is a 25% of passing on the sickle cell gene to your future children if diagnosed as a carrier of the gene.

If a carrier has 3 children what is the probability that all three children have the sickle cell gene?

What is the probability that one child inherits the sickle cell gene?

What is the probability that NONE of the three children have the gene?

13. Let x be uniform from 70-85

What is f(x)?

What is the mean?

What is the std?

What is the probability that x = 80?

13. Find the z-scores for:

90%

95%

99%

94%

98%

14. Construct a 95% confidence interval for data in which 4,400 people were sampled, the mean found was 5.15, and the std. found was 1.68.

15. The average time 15 adults spent watching TV in a week is 350 minutes. Suppose it is known the standard deviation of all adults watching TV is 20 minutes? Construct a 90% confidence interval.

16. Average time 35 adults spent watching TV is 350 minutes, their standard deviation was 20 minutes. Construct a 99% confidence interval.

17. Average time 12 adults spent watching TV was 350 minutes, their standard deviation was 20 minutes.

18. I played Fortnite and won 113/271 tries. This led to accusations of cheating and lying. What is the 95% confidence interval for true proportion?

19. Interested in true proportion of students who downloaded music illegally. In a sample of 200, 119 said they downloaded music illegally. What is 90% confidence interval of true proportion?

20. Anonymous poll of 377 UCF students, 21 reported to be from Georgia. In order to be within 2% of actual proportion at 95% confidence, how large of a sample size is needed?

21. Survey of shoppers is planned to see what % use credit cards. Prior surveys suggest 61% use. How many shoppers should be surveyed if you want margin of error to be 2% and want a 95% confidence interval?

22. Estimate proportion of people that wear seatbelts in Florida. If you need estimate to be within 2% of true proportion w/ 99% CI, how many people would you need to sample?

23. Supplement company claims their magic pill contains 58 milligrams of their magic compound. I take the pill and don’t feel the magic. I think there is less than 58 milligrams of magic within each pill and want to collect some data in order to prove my hypothesis to be correct. After sampling 36 pills and figuring out their doses, the average pill had 56 milligrams of magic, with a std. of 6. Using alpha .01, do we reject or fail to reject the null hypothesis?

24. Method for detecting breast cancer fails to detect the cancer in at least 20% of women who have the disease. 140 women w/ breast cancer were screened, the method failed to detect the breast cancer in 12 women. Is there evidence to contradict at a = 0.01?

25. Construct 95% confidence interval for difference in weight loss between the two groups

Group 1: n = 37 | mean loss = 27.1 | std. = 3.5 Group 2: n = 36 | mean loss = 16.8 | std = 5.2

26. Construct a 98% confidence interval for difference in blood pressure reduction after using two difference prescription pills.

Pill 1: n = 10 | mean reduction = 10 | std. = 0.8

Pill 2: n = 10 | mean reduction = 9.1 | std. = 0.7

27. Students and professors voted on a bill. This bill included one yes/no question. 200 students voted on the bill and 300 professors voted on the bill. While 80 students voted “yes” on the bill, 150 professors voted “yes” on the bill. Create a 99% confidence interval for the difference in true proportions

28. Past surveys of this kind have shown no statistically significant difference between students and professors voting on a bill. Using the data collected from the question above, as well as alpha = 0.01, can we reject this null hypothesis?