Suppose you want to test the claim that $\mu _ { 1 } \neq \mu _ { 2 }$ Assume the two samples are random and independent. At a level of significance of α = 0.02, when should you reject H₀?
Population statistics: $\sigma _ { 1 } = 0.76 \text { and } \sigma _ { 2 } = 0.51$ Sample statisticsstatistics: $\overline { \mathrm { x } } 1 = 1.8 , \mathrm { n } _ { 1 } = 51 \text { and } \overline { \mathrm { x } } 2 = 2.2 , \mathrm { n } _ { 2 } = 38$
A)Reject H₀ if the standardized test statistic is less than -2.33 or greater than 2.33.
B)Reject H₀ if the standardized test statistic is less than -1.96 or greater than 1.96.
C)Reject H₀ if the standardized test statistic is less than -1.645 or greater than 1.645.
D)Reject H₀ if the standardized test statistic is less than -2.575 or greater than 2.575.

Question

Quizplus · Accepted Answer

Given the level of significance α = 0.02 for a two-tailed test, the critical z-values that correspond to the rejection regions are found using the standard normal distribution. For a two-tailed test with α = 0.02, the significance level in each tail is α/2 = 0.01. Looking up the z-value for 0.01 in each tail of the standard normal distribution gives approximately ±2.33. Therefore, you reject H₀ if the standardized test statistic is less than -2.33 or greater than 2.33.

Suppose You Want to Test the Claim That μ1≠μ2\mu _ { 1 } \neq \mu _ { 2 }μ1​=μ2​

Suppose You Want to Test the Claim That $\mu _ { 1 } \neq \mu _ { 2 }$