Chapter 5 STATISTICS (PART 2)

Statistical Inferences Statistical inference is the process by which we infer population properties from sample properties. There are two types of statistical inference: • Estimation • Hypotheses Testing

estimation • Point Estimator: draws inferences about a population by The objective of estimation is to approximate the value of a population parameter based on sample population. For example, we want to estimate population mean µ (true mean) by using sample mean There are two types of estimators: • Point Estimator: draws inferences about a population by estimating the value of an unknown parameter using a single value or point.

Statistical estimation Interval Estimator : draws inferences about a population by estimating the value of an unknown parameter using an interval. Here, we try to construct an interval that “covers” the true population parameter with a specified probability. Confidence Intervals: The confidence level associated with a confidence interval states how much confidence we have that this interval contains the true population parameter. The confidence level is denoted by

Population Proportion Confidence Intervals Population Mean σ known Any size σ Unknown Population Proportion

Confidence Intervals To gain further insight into µ, we surround the point estimate with a margin of error: A CI for (when is known) given by :

Confidence Interval Estimates for Population Mean

Example 6.1

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Example 6. 2 : A publishing company has just published a new textbook Example 6.2 : A publishing company has just published a new textbook. Before the company decides the price at which to sell this textbook, it wants to know the average price of all such textbooks in the market. The research department at the company took a sample of 36 comparable textbooks and collected the information on their prices. this information produced a mean price RM 70.50 for this sample. It is known that the standard deviation of the prices of all such textbooks is RM4.50. Construct a 90% confidence interval for the mean price of all such college textbooks.

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Confidence Interval for Estimating a Population Proportion, p

To construct a confidence interval to measure the proportion p of a population that has a particular characteristic (e.g. supporters of President Obama): Step 1: Take a sample of size n, calculate (p-hat) as the sample proportion of people who have that characteristic (e.g. saying they support Obama in a survey) Step 2: Calculate the margin of error: Step 3: The 95% confidence interval:

Example 6.4: According to the analysis of Women Magazine in June 2005, “Stress has become a common part of everyday life among working women in Malaysia. The demands of work, family and home place an increasing burden on average Malaysian women”. According to this poll, 40% of working women included in the survey indicated that they had a little amount of time to relax. The poll was based on a randomly selected of 1502 working women aged 30 and above. Construct a 95% confidence interval for the corresponding population proportion.

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Exercise 6.6: In one question of the GSS in 2000, 1154 people were asked whether they would be willing to pay higher prices to support the environment. 518 said yes. Find a 95% confidence interval for p, the true proportion in the whole population who would be willing to pay higher prices to support the environment. Answer:(0.420,0.478) or 42% and 48%

Solution: Step 1: to 3 decimal places. Step 2: The standard error: Step 3: Margin of error : to 3 decimal places. The 95% confidence interval is . Conclusion: