Chapter 7

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Camosun College *

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Feb 20, 2024

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Ch7.2-7.5-page 1 7.2 Paired data Paired t-C.I., paired t-test Data format (n pairs of data from n subjects): Subject A B C D E Before (x) X 1 X 2 X 3 X 4 X 5 After (y) Y 1 Y 2 Y 3 Y 4 Y 5 X diff = x-y Let D µ = ____________________________________________________________ Confidence Interval for µ D : * diff diff df S x t n ± Test statistic : 0 diff D diff x t S n µ − = has t n-1 if n >30 or X diff is nearly normally distributed

Ch7.2-7.5-page 2 Example 1. Are textbooks actually cheaper online? Below are 6 textbooks’ prices in the UCLA bookstore and on Amazon. Book1 B2 B3 B4 B5 B6 UCLA (x) 27.67 40.59 31.68 16 23.76 27.70 Amazon (y) 27.95 31.14 32 11.52 28.74 18.22 a) Test the appropriate hypothesis to answer the question. b) Compute and interpret a 95% CI for the mean price difference between UCLA and Amazon.

Ch7.2-7.5-page 3 Class EX1. A dietitian wishes to see if a person’s cholesterol level will change if the diet is supplemented by a certain mineral. Six randomly selected subjects were pretested for cholesterol levels, and then they took the mineral supplement for a 6-week period. Their results resulted cholesterol levels (in mg per deciliter) are shown in the table below: Subject A B C D E F Before 210 235 208 190 172 244 After 190 170 210 188 173 228 Assume the populations of cholesterol levels are normally distributed. a) Can it be concluded that the cholesterol level has been changed at the 10% significance level? Answer the question by completing the following steps: Step 0 Compute the sample statistics Step 1 Define the parameter of interest and state the hypotheses. Step 2 Check the conditions needed to proceed with inference and calculate the test statistic . Step 3 Find the p-value.

Ch7.2-7.5-page 4 Step 4 Conclude H 0 and write a sentence to answer the question. b) Construct a 95% confidence interval for the true mean difference in Before and After . c) Conclude the hypotheses set up in part a) based on the confidence interval obtained above.

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