Confidence Interval You sample 36 apples from your farm’s harvest of over 200,000 apples. The mean weight of the sample is 112 grams (with 40 gram sample.

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Presentation transcript:

Confidence Interval You sample 36 apples from your farm’s harvest of over 200,000 apples. The mean weight of the sample is 112 grams (with 40 gram sample standart deviation). What is the probability that the mean weight of all 200,000 apples is within 100 and 124 grams?

Confidence Interval In a local teaching district a technology grant is available to teachers in order to install a cluster of four computers in their classrooms. From the 6250 teachers in the district, 250 were randomly selected and aske if they felt that computers were an essential teaching tool for their classrooms. Of those selected, 142 teachers felt that computers were an essential teaching tool. Calculate a 99% confidence interval for the proportion of teachers who felt that computers are an essential teaching tool. How could the survey be changed to narrow the confidence interval but to maintain the 99% confidence interval.»

Small sample size confidence intervals 7 patients’ blood pressures have been measured after having been given a new drug for 3 months. They had blood pressure increases of 1.5, 2.9, 0.9, 3.9, 3.2, 2.1, and 1.9. Construct a 95% confidence interval for the true expected blood pressure increase for all patients in a population.

Hypothesis Testing A neurologist is testing the effect of a drug on response time by injecting 100 rats with a unit dose of the drug, subjecting each neurological stimulus, and recording its repsonse time. The neurologist knows that the mean response time for rats not injected with the drug is 1.2 seconds. The mean of the 100 injected rats’ response times is 1.05 seconds with a sample standart deviation of 0.5 seconds. Do you think that the drug has an affect on response time?

Small sample hypothesis test The mean emission of all engines of a new design needs to be below 20 ppm if the design is to meet new emission requirements. Then engines are manufactured for testing purposes, and the emission level of each is determines. The emission data is: 15,616,222,520,516,4 19,416,617,912,713,9 Does the data supply sufficient evidence to conclude that this type of engine meets the news standart? Assume we are willing to risk a Type I error with probability = 0.01

Large Sample - Hypothesis Testing We want to test the hypothesis that more than 30 % of U.S. households have internet access (with a significance level of 5%). We collect a sample of 150 households and find that 57 have access.

Hypothesis Testing with two samples

Confidence Interval of Difference of Means We’re trying to test whether a new, low-dat diet actually helps obese people lose weight. 100 randomly assigned obese people are assigned to group 1 and put on the low fat diet. Another 100 randomly assigned obese people are assigned to group 2 and put on a diet of approximately the same amount of food, but not as low in fat. After 4 months, the mean wieght loss was 9,31 lbs. For group 1 (s=4,67) and 7,40 lbs. (s=4,04) for group 2. What is the 95% confidence interval for this research?