Question

Consider the following hypothesis statement using 0.10 and the following data from two independent samples. Complete parts a and b below Ho P-P20 x 67 x2 72 H pi P20 n 150 n2 180 Click of the st ormal table, Click here to view page 2 of the standard normal table. a. Calculate thee appropriate test statistic and interpret the result What is the test statistic? Round to two decimal places as needed.) What is/are the critical value(s)? (Round to two decimal places as needed. Use a comma to separate answers as needed.) Interpret the result Choose the correct answer below. O A. Do not reject H. There is insufficient evidence to support the statement that H, is true. O B. Do not reject H. There is evidence to support the statement that H, is true. O C. Reject Hp. There is evidence to support the statement that H, is true. O D. Reject Hp There is insufficient evidence to support the statement that H, is true b. Calculate the p-value and interpret the result. What is the p-value? Click to select your answer(s)

Answer 1

Here

$\hat{p_1} = \frac{67}{150} = 0.446667, n_1 = 150, \hat{p_2} = \frac{72}{180} = 0.4,n_2 = 180$

The test statistic can be written as

$z = \frac{\hat{p_1} - \hat{p_2}}{\sqrt{\frac{\hat{p_1}*(1-\hat{p_1})}{n_1} + \frac{\hat{p_2}*(1-\hat{p_2})}{n_2}}}$ which under H₀ follows a standard normal distribution.

We reject H₀ at 0.1 level of significance if $z_{obs} < -z_{0.1}$

Now,

The value of the test statistic $z_{obs} = 0.854718$

and critical value $z_{critical} = -z_{0.1} = -1.28155$

Since $z_{obs} = 0.854718 \nless z_{critical} = -1.28155$ , so we fail to reject H₀ at 0.1 level of significance.

Conclusion : A) Do not reject H₀. There is insufficient evidence to support the statement that H₁ is true.

b) p-value $=P(Z<z_{obs}) =P(Z< 0.854718) = \Phi(0.854718) = 0.803646$

Since P-value > 0.1, so we fail to reject H₀ at 0.1 level of significance.

Conclusion : A)Do not reject H₀. There is insufficient evidence to support the statement that H₁ is true.