In testing $H _ { 0 } : p _ { 1 } = p _ { 10 } , p _ { 2 } = p _ { 20 } , \ldots . . , p _ { 5 } = p _ { 50 }$ versus the alternative $H _ { \pm }$ that states that at least one $p _ { i }$ does not equal $p _ { 10 } ,$ rejection of $H _ { 0 }$ is appropriate at .10 significance level when the test statistic value $\chi ^ { 2 }$ is
A) greater than or equal to 9.236.
B) smaller than or equal to 11.070
C) between 9.236 and 11.070
D) smaller than or equal to 7.779
E) greater than or equal to 7.779

Question

Quizplus · Accepted Answer

In hypothesis testing, when using the chi-square ($\chi^2$) test statistic to compare observed frequencies with expected frequencies, the null hypothesis $H_0$ is rejected if the test statistic is greater than the critical value from the chi-square distribution table at the given significance level. Since the question specifies a significance level of .10 and is asking when to reject $H_0$, the correct choice involves a test statistic that is greater than a threshold value. Therefore, the answer is "greater than or equal to 7.779," because typically, for a chi-square test, higher values of the test statistic indicate a greater discrepancy between observed and expected frequencies, leading to rejection of the null hypothesis if the test statistic exceeds the critical value corresponding to the significance level.

In Testing H0:p1=p10,p2=p20,…..,p5=p50H _ { 0 } : p _ { 1 } = p _ { 10 } , p _ { 2 } = p _ { 20 } , \ldots . . , p _ { 5 } = p _ { 50 }H0​:p1​=p10​,p2​=p20​,…..,p5​=p50​

In Testing $H _ { 0 } : p _ { 1 } = p _ { 10 } , p _ { 2 } = p _ { 20 } , \ldots . . , p _ { 5 } = p _ { 50 }$