CH11 exercises solutions

CH11 exercises solutions - X X X X X X X X X X X X X X X X...

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X X X X X X X X X X X X X X X X AP Statistics Packet 11 X Inference for Distributions Inference for the Mean of a Population Comparing Two Means X X X X X X
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HW #19 1 – 4, 7 - 10 11.1 Writers in some fields often summarize data by giving x and its standard error rather than x and s. The standard error of the mean x is often abbreviated as SEM. (a) A medical study finds that x = 114.9 and s = 9.3 for the seated systolic blood pressure of the 27 members of one treatment group. What is the standard error of the mean? 1.7898 s n 9.3 = = 27 (b) Biologists studying the levels of several compounds in shrimp embryos reported their results in a table, with the note, “Values are means ± SEM for three independent samples.” The table entry for the compound ATP was 0.84 ± 0.01. The researchers made three measurements of ATP, which had x = 0.84. What was the sample standard deviation s for these measurements? Since 0.01 , 0.0173 3 s s = = 11.2 What critical value t * from Table C satisfies each of the following conditions? (a) The t distribution with 5 degrees of freedom has probability 0.05 to the right of t * . 2.015 (invT (.95, 5)) (b) The t distribution with 21 degrees of freedom has probability 0.99 to the left of t * . 2.518 (invT (.99, 21)) 11.3 What critical value t * from Table C satisfies each of the following conditions? (a) The one-sample t statistic from a sample of 15 observations has probability 0.025 to the right of t * . 2.145 (invT (.975, 14)) (b) The one-sample t statistic from an SRS of 20 observations has probability 0.75 to the left of t * . 0.688 (invT (.75, 19)) 11.4 What critical value t * from Table C should be used for a confidence interval for the mean of the population in each of the following situations? (a) A 90% confidence interval based on n = 12 observations. df = 11, t * = 1.796 (a) A 95% confidence interval from an SRS of 30 observations. df = 29, t * = 2.045 (a) An 80% confidence interval from a sample of size 18. df = 17, t * = 1.333
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11.7 The one-sample t statistic for testing 0 :0 A H H m m = from a sample of n = 15 observations has the value t = 1.82. (a) What are the degrees of freedom for this statistic? df = 14 (b) Give the two critical values t * from Table C that bracket t. What are the right-tail probabilities p for these two values? 1.82 is between 1.761 ( p = 0.05) and 2.145 ( p = 0.025). (c) Between what two values does the P- value of the test fall? The P- value is between 0.025 and 0.05 (in fact, p = tcdf( 1.92, , 14) = 0.0451). (d) Is the value t = 1.82 statistically significant at the 5% level? At the 1% level? t = 1.82 is significant at α = 0.05 but not at α = 0.01. 11.8 The one-sample t statistic from a sample of n = 25 observations for the two-sided test of 0 : : A H H m m = 64 ≠ 64 has the value t = 1.12. , (a) What are the degrees of freedom for this statistic? df = 24 (b) Give the two critical values t * from Table C that bracket t. What are the right-tail probabilities p for these two values? 1.12 is between 1.059 ( p = 0.15) and 1.318 ( p = 0.10). (c) Between what two values does the P- value of the test fall? (Note that A H is two-sided.) The P- value is between 0.30 and 0.20 (in fact, p = 2tcdf( 1.12, , 24) = 0.2738).
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This note was uploaded on 12/09/2011 for the course STAT 101 taught by Professor O during the Fall '08 term at Lake Land.

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CH11 exercises solutions - X X X X X X X X X X X X X X X X...

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