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Review – Exam 3

Review – Exam 3. Confidence Intervals Hypothesis Testing Linear Regression. Review Question . Cell phones have a mean weight, Ч , of 5.7 ounces and a standard deviation, σ , of 2.0 ounces. We randomly sample 49 cell phones.

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Review – Exam 3

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

  2. Review Question • Cell phones have a mean weight, Ч, of 5.7 ounces and a standard deviation, σ, of 2.0 ounces. • We randomly sample 49 cell phones. • What is the probability that the mean of our sample will be >6.2 ounces? • If the sample size had been 12, what further assumption must we make in order to solve this problem?

  3. Review Question • 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%?

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

  5. 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?

  6. Review Question • A regional office of the IRS randomly distributes returns to be audited to the pool of auditors. Over the thousands of returns audited last year, the average amount of extra taxes collected was $356 per audited return. One of the auditors, Mr. Claus, is suspected of being too lenient with his audits. For a simple random sample of 30 of Mr. Claus’s audited returns, an average of $322 in extra taxes was collected with a sample standard deviation of $90. Based on this information and a confidence level of 0.95, do the suspicions regarding Mr. Claus appear to be true?

  7. 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?

  8. 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?

  9. 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 T P Height 10 69.30 4.37 1.38 (66.17, 72.43) 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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