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Review – Exam 3

Review – Exam 3. Confidence Intervals Hypothesis Testing Linear Regression. Sampling Distributions. n =9 n =36. Practice.

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Review – Exam 3

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  1. Review – Exam 3 Confidence Intervals Hypothesis Testing Linear Regression

  2. Sampling Distributions n=9 n=36

  3. Practice • The average weight of a cell phone is 5.7 ounces. Assuming a population σ of 2.0 ounces and a random sample of 49 phones, what is the probability the average weight for the sample will be ≥ 6.2 ounces? • If the sample size had been 12 instead of 49, what further assumption must we make in order to solve this problem?

  4. Using the t-table • For a sample size of n = 22, what t values would correspond to an area centered at t = 0 and having an area beneath the curve of 90%? • For a sample size of n = 200, what t values would correspond to an area centered at t = 0 and having an area beneath the curve of 95%?

  5. Confidence Interval • A random sample of 30 students has been selected from those attending EOCC. The average number of hours they spent in the school library last week was 5.21 with a sample standard deviation of 1.18 hours. • Construct a 90% confidence interval for the population mean.

  6. Sample Size • A package-filling machine has been found to have a standard deviation of 0.65 ounces. A random sample will be conducted to determine the average weight of product being packed by the machine. • To be 95% confident that the sample mean will not differ from the actual population mean by more than 0.1 ounces, what sample size is required?

  7. Formulate the Hypothesis • I predict the mean score for the next exam will be 92% or higher. The mean turns out to be 90%. Was I wrong? • The owner of the Montgomery Biscuits claims average attendance at home games is 3,456. A survey of the 12 home games in July showed average attendance to be 3,012. Was the owner’s claim accurate? • My employee stated that less than 25% of the people working in Daleville are in a retirement plan. A survey of 20 employees shows only 4 are in a plan. Was the boss correct?

  8. Testing Error • I predict the population mean score for an exam will be 92%. After taking a sample of 8 and finding the mean score from the sample to be 99.4%, I conduct a t-test at a .90 significance level and reject the null hypothesis. • After teaching the same class for many years and giving the same exam, I discover that the mean for all students is very close to 92%. • What type of error did I make with the results of the first t-test? Why?

  9. Hypothesis Testing • Joe’s Tire Company claims their tires will last at least 60,000 miles in highway driving conditions. • The editors of Tire magazine doubt this claim, so they select 31 tires at random and test them. The tires they tested had a mean life of 58,341.69 miles and a standard deviation of 3,632.53 miles. • Is Joe’s claim accurate?

  10. p-value My null hypothesis is that the population mean height = 66 inches One-Sample T: Height Test of mu = 66 vs not = 66 Variable N Mean StDev SE Mean 95% CI Height 10 69.30 4.37 1.38 (66.17, 72.43) T P 2.39 0.041 Consider a significance level of .05. Based on this sample data, should I accept or reject my null hypothesis? Why?

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