$$ H_{0}: \rho=0 $$ $$ H_{a}: \rho0 $$ A hypothesis test was conducted and a test statistic of $$ z= $$ 1.062 was computed. Use Minitab to find the p value for this right-tailed test. Round your answer to three decimal places.

Question

$$ H_{0}: \rho=0 $$ $$ H_{a}: \rho>0 $$ A hypothesis test was conducted and a test statistic of $$ z= $$ 1.062 was computed. Use Minitab to find the p value for this right-tailed test. Round your answer to three decimal places.

UpStudy AI · Accepted Answer

1. The null and alternative hypotheses are given as:
   - $$ H_{0}: \rho = 0 $$
   - $$ H_{a}: \rho > 0 $$
   
2. The test statistic is $$ z = 1.062 $$.

3. For a right-tailed test, the p-value is defined as:
   $$
   p\text{-value} = P(Z > 1.062) = 1 - \Phi(1.062)
   $$
   where $$\Phi(1.062)$$ denotes the cumulative distribution function of the standard normal distribution at $$ z = 1.062 $$.

4. Using Minitab or a standard normal table, we find:
   $$
   \Phi(1.062) \approx 0.855
   $$
   
5. Therefore, the p-value is:
   $$
   p\text{-value} = 1 - 0.855 \approx 0.145
   $$

6. Rounding to three decimal places, the p-value is $$ 0.145 $$.
The p-value for the right-tailed test is 0.145.

\( H_{0}: \rho=0 \) \( H_{a}: \rho>0 \) A hypothesis test was conducted and a test statistic of \( z= \) 1.062 was computed. Use Minitab to find the p value for this right-tailed test. Round your answer to three decimal places.

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