1. MM207 Statistics Welcome to the Unit 9 Seminar With Ms. Hannahs Final Project is due Tuesday, August 7 at 11:59 pm ET. No late projects will be accepted.

2. Unit 5 Correlation Coefficient Line of Best Fit Predicting a value based on the Best Fit line

3. Types of Correlations 1.Positive: x and y move in the same direction 2.Negative: x and y move in opposite directions 3.Zero: no pattern of movement in x and y 4.Nonlinear relationship: The two variables are related, but the relationship results in a scatter diagram that does not follow a straight-line pattern.

4. Example: Use the best fit line to predict the value of y at x = 30. a.18b.19c.20d.22

5. Scatter Plots and Correlation in MSL StatCrunch You can make a scatter plot by Choosing Graphics-> Scatter Plot. Be sure to choose the correct column for variable x and for variable y. Click Create Graph to get

6. Scatter Plots and Correlation in MSL StatCrunch Data now in worksheet You can compute values using Select the 2 columns to correlate and choose Calculate to get the value as shown below.

7. Best Fit Lines in MSL StatCrunch What is the best fit line for using waist to predict weight? weight = 2.37(waist) – 44.08. Use this to predict. If waist = 90 cm, then weight = (2.37)(90) - 44.08 = 169.22 lbs

8. Unit 6 Finding a z-score Using Statcrunch to find a zscore Using Statcrunch to find a ¯ probability Making inferences from a normal calculation probability

9. Computing Standard Scores The number of standard deviations a data value lies above or below the mean is called its standard score (or z-score), defined by z = standard score = = (x – µ) / σ This formula is used when the sample size, n = 1 The standard score is positive for data values above the mean and negative for data values below the mean. data value – mean standard deviation

10. The Central Limit Theorem Suppose we take many random samples of size n for a variable with any distribution (not necessarily a normal distribution) and record the distribution of the means of each sample. Then, 1.The distribution of means will be approximately a normal distribution for large sample sizes. n>30 is magic number 2.The mean of the distribution of means approaches the population mean, µ, for large sample sizes. 3.The standard deviation of the distribution of means approaches σ/√n for large sample sizes, where σ is the standard deviation of the population.

11. Computing Standard Scores data value – mean standard deviation

12. Computing Probabilities in MSL EASY! Example 1 Note: the icon here is not data for the problem but a standard scores for the specific distribution given in this problem.

13. Example 1-Part a: find the percentage of scores greater than 1866. Choose Calculator -> Normal then put in the mean, st dev and value in question, 1866. Be sure to choose => for “greater than or equal”. Click Compute to get the graph and answer shown in the second picture below. The answer is.15865 which as a percentage is 15.865 and rounds to 15.87% with two decimals as asked for in the question.

14. Example 2 - find the probability the mean blood pressure is less than 111 for a sample of 280 women. Since n > 1, this is Central Limit Theorem. Be sure to compute new Standard deviation as sigma / sqrt(n) before plugging into StatCrunch. Standard deviation = 13.22 / sqrt(280) = 13.22 / 16.73 =.79 ~.8

15. Unit 7 How to make a contingency table Finding probability Finding Conditional Probability Finding Probability of One event AND another Finding Probability of One event OR another

16. Contingency table

17. Mutually Exclusive Events and the Rule of OR (addition rule) Only one selection is made For ANY events A OR B from a sample space S P(A or B) = P(A) + P(B) – P(A and B) For mutually exclusive events A, B from a sample space S, P(A or B) = P(A) + P(B)

18. Independent Events and the Rule of AND (multiplication rule) Two events A AND B will occur in sequence Independent events - one of the Events does not affect the probability of the occurrence of the other Probability of A AND B when Dependent P(A and B) = P(A) * P(B|A) Probability of A AND B when Independent P(A and B) = P(A) * P(B)

19. Unit 8 Finding confidence Intervals Determining the Margin of Error Finding the minimum sample size.

20. Create Confidence Interval for a mean At one hospital, a random sample of 100 women giving birth to their first child is selected. Among this sample, the mean age was 25.7 with a standard deviation of 5.1. Estimate the mean age of all women giving birth to their first child at this hospital. Give the 95% confidence interval two decimal places. margin of error = E ≈ 2s n2s n Next, we can write this confidence interval as xbar – E < μ < xbar + E See the technical note on page 347 the precise value is 1.96 and not 2. Let StatCrunch do it’s thing on the final.

21. Here we get 24.70 < µ < 26.70 because StatCrunch uses the precise 1.96 value and not the estimate of 2 as the textbook shows. Confidence Intervals for Means in StatCrunch

22. Create Confidence Interval for a proportion For a population proportion, the margin of error for the 95% confidence interval is Next, write this confidence interval more formally as p-hat – E < p < p-hat + E *See the technical note on page 356 the precise value for a 95% confidence interval is 1.96 and not 2. Let StatCrunch do it’s thing on the final. p-hat The Nielsen ratings for television use a random sample of households. A Nielsen survey results in an estimate that a women’s World Cup soccer game had 72.3% of the entire viewing audience. Assuming that the sample consists of n = 5,000 randomly selected households, find the margin of error and the 95% confidence interval for this estimate.

23. Here we get.710 < p <.735 because StatCrunch uses the precise 1.96 value and not the estimate of 2 as the textbook shows. Let StatCrunch do it’s thing. You can find the margin Of error the same way we did before also. E = (.7354043 -.7105957)/ 2 =.0124 CI’s for Proportions in StatCrunch Select the level

24. Core Logic of Hypothesis Testing Considers the probability that the result of a study could have come about if the experimental procedure had no effect If this probability is low, scenario of no effect is rejected and the theory behind the experimental procedure is supported

25. Hypothesis Testing using Confidence Intervals  State the claim about the population mean  Determine desired confidence level  Select a random sample from the population  Calculate the confidence interval for the desired level of confidence.  If the claim is contained within the interval, the claim is reasonable; if it is not within the interval, the claim is not reasonable, at the given level of confidence.  See Testing a Claim document in Doc Sharing