10.2 Means sd Unknown

# Frequently used too difficult to population mean

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Unformatted text preview: imator standard error Hypothesis Tests margin of error interval estimate degrees of freedom Not frequently used —too difficult to Population Mean verify that population standard deviations μ are equal x If it can be assumed s σx =2, then: that σ1 = σ n • standard error can s be calculated from tα 2 the pooled n sample variance s • x ±tα 2 the degrees of n freedom calculated as: n1 + n2 – 2 n1 − Difference Between 2 Population Means D = μ1 – μ2 d x− 2 =1 x s= p n )1 n )2 ( 1 −1s2 +( 2 −1s2 n +n −2 1 2 tα 2 s 2 s22 1 + n n2 1 d ±tα 2 s2 s22 1 + nn 1 2 d= + − f nn 2 1 2 Example Specific Motors of Detroit has developed a new automobile known as the M car. 24 M cars and 28 J cars (from Japan) were road tested to compare mpg performance. The sample statistics are shown to the right: M Cars J Cars n x 24 28 29.8 27.3 s 2.56 1.81 Hypothesis Tests Example Specific Motors of Detroit has developed a new automobile known as the M car. 24 M cars and 28 J cars (from Japan) were road tested to compare mpg performance. The sample statistics are shown to the right: M Cars J Cars n x 24 28 29.8 27.3 s 2.56 1.81 Hypothesis Tests Example Specific Motors of Detroit has developed a new automobile known as the M car. 24 M cars and 28 J cars (from Japan) were road tested to compare mpg performance. The sample statistics are shown to the right: M Cars J Cars n x 24 28 29.8 27.3 s 2.56 1.81 Hypothesis Tests Example Specific Motors of Detroit has developed a new automobile known as the M car. 24 M cars and 28 J cars (from Japan) were road tested to compare mpg performance. The sample statistics are: M Cars J Cars Hypothesis Tests n x 24 28 29.8 27.3 s 2.56 1.81 Example Specific Motors of Detroit has developed a new automobile known as the M car. 24 M cars and 28 J cars (from Japan) were road tested to compare mpg performance. The sample statistics are: M Cars Hypothesis Tests n x s J Cars 24 28 29.8 27.3 2.56 1.81 Difference Between 2 Population Means parameter D = μ1 – μ2 point estimate d x− 2 =1 x standard error s 2 s22 sd = 1 + n n2 1 margin of error interval estimate s 2 s22 1 + n n2 1 tα 2 d ±tα 2 degrees of df = freedom ( s12 n1 22 s2 s 2 1 +2 n n2 1 2 + sn22 ) 2 ( )+ ( ) s1 1 n1 −1 n1 s2 2 1 n2 −1 n2 2 Example What is the parameter for the interval estimate? Specific Motors of Detroit has 2 developed D=µautomobile a new1 −µ known D the=µ −µ M cars as M car. 24 M−J M J and 28 J cars (from Japan) were road tested to compare mpg performance. The sample statistics are: M Cars Hypothesis Tests n x s J Cars 24 28 29.8 27.3 2.56 1.81 Difference Between 2 Population Means parameter D = μ1 – μ2 point estimate d x− 2 =1 x standard error s 2 s22 sd = 1 + n n2 1 margin of error interval estimate s 2 s22 1 + n n2 1 tα 2 d ±tα 2 degrees of df = freedom ( s12 n1 22 s2 s22 1 + nn 1 2 + s2 2 n2 ) 2 ( )+ ( ) s1 1 n1 −1 n1 s2 2 1 n2 −1 n2 2 Example Given these samples, what is the point estimate for the difference between the 2 population means (i...
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## This document was uploaded on 03/05/2014.

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