# 27 1754 ƒ william sealy gossett william sealy

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predicted the day of his death, Nov. 27, 1754. ¤ § ¥ ƒ William Sealy Gossett William Sealy Gossett was born on June 13, 1876, in Canterbury, Eng- land. Gossett earned a degree in chemistry from New College in Oxford in 1899. He then got a job as a chemist for the Guinness Brewing Com- pany. Gossett, along with other chemists, was asked to find a way to make the best beer at the cheapest cost. This allowed him to concen- trate on statistics. In 1904, Gossett wrote a paper on the brewing of beer that included a discussion of standard errors. In July, 1905, Gossett met with Karl Pearson to learn about the theory of standard errors. Over 15

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the next few years, he developed his t -distribution. The Guinness Brewery did not allow its employees to publish, so Gossett published his research using the pen name Student. Gossett died October 16, 1937. 16
Use nonparametric methods (not included in this chapter). start Are the two samples dependent ? Do n 1 and n 2 both exceed 30 ? Are both populations normally distributed ? Are σ 1 and σ 2 both known ? After applying the F test. What do we conclude about σ 1 2 = σ 2 2 ? Yes Yes Yes No Yes No No No Reject σ 1 2 = σ 2 2 Fail to reject σ 1 2 = σ 2 2 Testing Hypotheses Made about the Means of Two Populations 3 1 2 ~ Choosing an appropriate statistic for inference about μ 1 - μ 2

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AMS 315/576 Test 4 1. Do fraternities help or hurt your academic progress at college? To investigate this question, 5 students who joined fraternities in 1998 were randomly selected. It was found that their GPA before and after they joined the fraternities are as follows: Student 1 2 3 4 5 Before 3 4 3 3 2 After 2 3 3 2 1 (a) Please test the research hypothesis at the significance level 0.05 (b) What assumption(s) did you assume in the above test? 2. The Food and Drug Administration (FDA) wants to compare the mean caffeine contents of two brands of 6-oz. cola, Pepsi and Shasta. A typical test is the following: 5 cans of each brand were randomly selected. The results (in ounces) are as follows: (a) Please construct a confidence interval for the difference between the mean caffeine contents of Pepsi and Shasta. (b) At the significance level 0.05, can you conclude that the mean caffeine contents of Pepsi and Shasta are different? 3. A local eat-in-pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that the home delivery would be successful if the average time spent on the deliveries does not exceed 38 minutes. The owner has randomly selected 36 customers and has delivered pizza to their homes. He found that the average delivery time was 35 minutes with a standard deviation of 5 minutes. (a) At the significance level 0.05, can you conclude that the average delivery time would not exceed 38 minutes? (b) What is the P-value of your test? (c) Please construct a 95% confidence interval for the mean delivery time. 1. Paired-Samples, Small Sample Sizes 0.8, .447, 5, .05 d d X S n α = = = (a) 0 : 0 , : 0.
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