10.2 Means sd Unknown

# Specific motors of detroit has developed a new

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Unformatted text preview: 90% confidence interval estimate for the difference between the 2 population means? 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 DM–J = μM – μJ parameter point estimate d x −J= 5 =M x 2 . standard error s 2 s2 s = M + J =06 5 .2 d n n M J margin of error s 2 s2 M + J = .0 3 15 n n M J t0.102 interval estimate degrees of df = freedom s2 s22 1 + nn 1 2 d ±tα 2 ( + ) ≈40 ( )+ ( ) sM2 nM sM2 1 nM − nM 1 2 sJ 2 nJ 2 sJ 2 1 nJ − nJ 1 2 Example Given these samples, what is the 90% confidence interval estimate for the difference between the 2 population means? Hypothesis Tests 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: s12 s2 2 d ± Cars + J Cars M tα 2 n1 n 2 2 n 24 s 2 s28 M J t 0.10 2 x d ± 29.8 n + 27.3 n M s Difference Between 2 Population Means DM–J = μM – μJ parameter point estimate d x −J= 5 =M x 2 . standard error s 2 s2 s = M + J =06 5 .2 d n n M J margin of error s 2 s2 M + J = .0 3 15 n n M J t0.102 J 2 .5 ± 2.56 1.053 1.81 1.448 ≤ D0 ≤ 3.553 interval estimate degrees of df = freedom s2 s22 1 + nn 1 2 d ±tα 2 ( + ) ≈40 ( )+ ( ) sM2 nM sM2 1 nM − nM 1 2 sJ 2 nJ 2 sJ 2 1 nJ − nJ 1 2 Example Given these samples, what is the 90% confidence interval estimate for the difference between the 2 population means? 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: Hypothesis Tests We are 90% J Cars confident M Cars that the mean 28 n 24 dxifference in mpg 29.8 27.3 between the 2 cars is s 2.56 1.81 between 1.448 and 3.553 mpg. Difference Between 2 Population Means DM–J = μM – μJ parameter point estimate d x −J= 5 =M x 2 . standard error s 2 s2 s = M + J =06 5 .2 d n n M J margin of error s 2 s2 M + J = .0 3 15 n n M J t0.102 interval estimate degrees of df = freedom s2 s22 1 + nn 1 2 d ±tα 2 ( + ) ≈40 ( )+ ( ) sM2 nM sM2 1 nM − nM 1 2 sJ 2 nJ 2 sJ 2 1 nJ − nJ 1 2 Hypothesis Tests about the Difference between Two Population Means (σ1 and σ2 unknown) difference between 2 population means: D = μ1 – μ2 to ◦ ◦ make inferences about D, d x− 2 =1 x take independent simple random samples from 2 populations use sampling distribution of Hypothesis Tests ◦ use s1 and s2 to estimate population standard deviations use t-distribution for making inferences decision rules for hypothesis test based on either p-value or critical value approach calculate test statistic and decide based on decision rule Hypothesis Tests about the Difference between Two Population Means (σ1 and σ2 unknown) Population Mean test statistic upper tail test tSTAT = x −µ 0 sn degrees of freedom = n – 1 H0: μ ≤ μ0 Ha: μ &gt; μ0 reject H0 if tSTAT &gt; tα or p-value&lt;α Hypothesis Tests lower tail test H0: μ ≥ μ0 Ha: μ &lt; μ0 reject H0 if tSTAT &lt;– tα or p-value&lt;α two-tailed test H0: μ = μ0 Ha: μ ≠ μ0 reject H0 if tSTAT &lt; –tα/2 or tSTAT &gt; tα/2 or if p-value&lt;α Recall from chapter 9 Hypothesis Tests about the Difference between Two Population Means (σ1 and...
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