# One of the central questions that guinness wanted to

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One of the central questions that Guinness wanted to understand was which barley would be the best. From his research, Gossett realized that differences in the data could be due to natural variation or accidental in nature. Gossett also inferred that the resulting differences could be the product of the difference in how the barley was treated or perhaps just due to natural variation. On the other hand, the anomalies could also be the result of divergences in how the barley was treated or processed, which if addressed could lead to better methods of distillation. To determine the best barley solution, Gossett inferred that new statistical methods would need to determine the answer. He developed many of the methods that were needed to answer those questions. Gossett went on to spend a year at University College in London during his time while working at the brewery. He subsequently published his research under the name of
" Student " because Guinness would not allow him to use his own name. He is known as a founder of statistical inference, and his work with small samples came to be known as the Student t-test . Interactive Examples 1 1 What is the critical value for a 92% confidence level?
2 What is the confidence level for a critical value of -1.85?
3 About what portion of observations is covered by ± three standard deviations around the mean?
4 Construct a 96% confidence interval if a sampling distribution has a mean of 20, standard deviation of 5, and size of 100?
1
What is the critical value for a 92% confidence level?
2 Which of the following is true regarding a confidence interval for the population mean?
3 Which of the following may not be available when constructing a confidence interval?
4 Construct a 96% confidence interval if a sampling distribution has a mean of 10, standard deviation of 2, and size of 36?
5 About what portion of observations is covered by ± one standard deviation around the mean?
6 Put the steps below in calculation of a confidence interval from left to right.
Find the value of the critical value for the given confidence level Use the population standard deviation if known, otherwise use the sample standard deviation Apply the values to the equation for the confidence interval 7 Which of the following factors does a confidence interval depend on?