In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada claims that the current unemployment rate is lower than that of April 2011.Suppose a test was conducted on current unemployment and a random sample size of 1000 and found unemployment at 6.1%.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed. A) $\mathrm { H } _ { 0 }$ : p = 0.076; $\mathrm { H } _ { \mathrm { A } }$ : p 0.076; z = -1.79; P-value = 0.9633.This data shows no evidence that the unemployment rate has decreased since April of 2011. B) $\mathrm { H } _ { 0 }$ : p = 0.076; $\mathrm { H } _ { \mathrm { A } }$ : p

Question

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada claims that the current unemployment rate is lower than that of April 2011.Suppose a test was conducted on current unemployment and a random sample size of 1000 and found unemployment at 6.1%.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed. A) $\mathrm { H } _ { 0 }$ : p = 0.076; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.076; z = -1.79; P-value = 0.9633.This data shows no evidence that the unemployment rate has decreased since April of 2011. B) $\mathrm { H } _ { 0 }$ : p = 0.076; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.076; z = 1.79; P-value = 0.0367.This data shows very weak evidence that the unemployment rate has decreased since April of 2011. C) $\mathrm { H } _ { 0 }$ : p = 0.076; $\mathrm { H } _ { \mathrm { A } }$ : p ? 0.076; z = -1.79; P-value = 0.0734.This data shows moderate evidence that the unemployment rate has decreased since April of 2011. D) $\mathrm { H } _ { 0 }$ : p = 0.076; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.076; z = -1.79; P-value = 0.0367.This data shows strong evidence that the unemployment rate has decreased since April of 2011. E) $\mathrm { H } _ { 0 }$ : p = 0.076; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.076; z = 1.79; P-value = 0.9633.This data shows strong evidence that the unemployment rate has decreased since April of 2011.

Quizplus · Accepted Answer

The correct null hypothesis ($H_0$) should state the unemployment rate is equal to the April 2011 rate (7.6% or 0.076), and the alternative hypothesis ($H_A$) should state the current rate is less than the April 2011 rate, reflecting the claim that the unemployment rate has decreased. The negative z-score (-1.79) indicates the sample mean is below the hypothesized mean, and a P-value of 0.0367 suggests there is strong evidence against the null hypothesis at common significance levels (e.g., 0.05), supporting the claim that the unemployment rate has decreased.

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