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Exam 2 Review

Exam 2 Review. Sampling. A company is trying to see if it it’s customers would prefer to expand their clothing section or their home store section. Since they are a national company, performing a census is unrealistic and therefore they will survey a sample.

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Exam 2 Review

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  1. Exam 2 Review

  2. Sampling

  3. A company is trying to see if it it’s customers would prefer to expand their clothing section or their home store section. Since they are a national company, performing a census is unrealistic and therefore they will survey a sample.

  4. Randomly select one store and ask 30 of the customers at this store their opinion • Simple Random Sample • Stratified Random Sample • Systematic Sampling • Cluster Sampling

  5. Put an advertisement in the newspaper asking people to mail in their vote • Simple Random Sample • Voluntary Response Sample • Convenience Sample • Stratified Random Sample

  6. Send a survey to every customer’s home and ask the customer to fill it out and return it • Simple Random Sample • Voluntary Response Sample • Convenience Sample • Stratified Random Sample

  7. Go through the company’s records, selecting every 100th customer. Survey every person chosen. • Simple Random Sample • Stratified Random Sample • Systematic Sampling • Cluster Sampling

  8. Randomly select 20 customers from each store. Send each a survey and follow up with a phone call if they do not return the survey within a week • Simple Random Sample • Stratified Random Sample • Systematic Sampling • Cluster Sampling

  9. Sponsor a commercial during a TV program and ask people to call in their preferences. • Simple Random Sample • Voluntary Response Sample • Convenience Sample • Stratified Random Sample

  10. Go through the company’s records, and select a random 100 customers. Survey every person chosen. • Simple Random Sample • Stratified Random Sample • Systematic Sampling • Cluster Sampling

  11. Central Limit Theorem

  12. CLT • In a non-normal distribution, the sample means will fall normally around the population mean. (If, the sample means are obtained from random samples with size 30 or larger.) • 2 conditions: • Large Sample Size (n>30) • Simple Random Sample

  13. The life expectancy in America is non - normal with an average of 72years and a standard deviation of 15 years. • What is the probability that a randomly selected American will live to be 80 years old. • What is the probability that you will have obtain a random sample of 45 people with a sample mean of 98 years.

  14. Confidence Intervals

  15. () ) ) • Known Standard Error () • () ) ) • Estimated standard error ()

  16. A box of Lucky Charms promises an average 15 oz of cereal per box. You want to test this claim, so you tested a sample of 40 boxes. The average amount of cereal in these 40 boxes was 13 ozwith an estimated s = 8.8oz. • Create a 95% confidence interval for your estimated average. • Do you think the company is holding up to their promise?

  17. Which sentences properly Interpret this confidence interval??? In trying to predict average body temperature of Americans, I got a 95% confidence interval of… ( 96.9 99.3) • I am 95% confident the average body temperature of an American is between 96.9 and 99.3 degrees. • 95% of Americans have a body temperature between 96.9 and 99.3 degrees • The average body temperature of an American is between 96.9 and 99.3 degrees. • 95% of samples have an average between 96.9 and 99.3 • 95% of confidence intervals from the samples I take will contain the true average American body temperature.

  18. Interpretation • I am 95% that ______(your parameter)____ is between ______ and ______

  19. Hypothesis Testing

  20. The average college student pays $20,335 per year in tuition. In order to see if Iowa State costs are less than the national average, a random sample of 100 ISU students is taken. • What is • What is

  21. The average college student pays $20,335 per year in tuition. In order to see if Iowa State costs are less than the national average, a random sample of 100 ISU students is taken. Your sample of 100 students pays an average of $18,856 and has a sample standard deviation of $8,750. • When you run a hypothesis test you obtain the following output… t-stat -2.83 p-value t 0.006 P-value < t 0.003 P-value > t 0.997 What can you conclude about ISU tuition costs?

  22. Putting it all together

  23. The situation You are DISH Network. You are trying to decide whether to offer a new sports channel. You are willing to offer it if it seems to have a customer ranking of at least 7.5 (out of 10).

  24. Basics • What is the population? • What is your parameter? • You are DISH Network. You are trying to decide whether to offer a new sports channel. You are willing to offer it if it seems to have a customer ranking of at least 7.5 (out of 10).

  25. You are DISH Network. You are trying to decide whether to offer a new sports channel. You are willing to offer it if it seems to have a customer ranking of at least 7.5 (out of 10). • You decide to take a sample of 125 of your customers. • What type of sample should you take? • Can you still make assumptions even if the population distribution is non-normal?

  26. Null and Alternative Hypothesis • You are DISH Network. You are trying to decide whether to offer a new sports channel. You are willing to offer it if it seems to have a customer ranking of at least 7.5 (out of 10). What is your Null hypothesis and alternative hypothesis?

  27. Confidence interval • You are DISH Network. You are trying to decide whether to offer a new sports channel. You are willing to offer it if it seems to have a customer ranking of at least 7.5 (out of 10). You take a 125-customer random sample • Your sample yields an average of a 6.8 rating. Your sample standard deviation is 2.15. • Create a 95% confidence interval for the population parameter.

  28. HypothesisTest • You are DISH Network. You are trying to decide whether to offer a new sports channel. You are willing to offer it if it seems to have a customer ranking of at least 7.5 (out of 10). You take a 125-customer random sample You perform a hypothesis test with on your hypothesis based on your sample and these are the test results… t-stat = -3.64 p-value < t = 0.043 p-value > t = 0.957 p-value t = 0.086

  29. Conclusion • Are you going to offer this new sports channel? • Using confidence interval • Using your hypothesis test

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