Question

The test statistic of z= 1.27 is obtained when testing the claim that p>0.7. a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. Find the P-value. c. Using a significance level of a = 0.05, should we reject H, or should we fail to reject H,? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. a. This is a right-tailed test. b. P-value = (Round to three decimal places as needed.) c. Choose the correct conclusion below. O A. Reject Ho. There is not sufficient evidence to support the claim that p>0.7. B. Fail to reject Ho. There is not sufficient evidence to support the claim that p>0.7. OC. Reject Ho. There is sufficient evidence to support the claim that p>0.7. OD. Fail to reject Ho. There is sufficient evidence to support the claim that p>0.7.

Answer 1

1. a) right tailed test, as the alternative hypothesis contains " > " sign.

b) P-value

$=P(Z>z_{obs}) = P(Z>1.27) = 1 - P(Z\leq 1.27) = 1 - \Phi(1.27) = 1 - 0.898 =0.102$

c) Since P-value > 0.05, so we fail to reject H₀ at 5% level of significance.

ans->B)

2.

Let p denotes the population proportion. Hypotheses : To test null hypothesis H. :p=0.2 against alternative hypothesis H1 :p > 0.2 Let p denotes the sample proportion and n denotes the sample size. Here, p 53 249 = 0.2129, n=249, standard error 0.2 + (1 -0.2) 249 0.025349 The test statistic can be written as: (p-po) Po*(1-P) n which under H, follows a standard normal distribution. Decision rule / Rejection region : We reject H, at 0.01 level of significance if P-value < 0.01 or if ZSTAT > 20.01 = 2.326348 0.4- 0.3 0.2 0.1- 0.0 -2 0 Z Now, Value of test statistic: The value of the test statistic 2STAT 0.506979 0.507 (0.2129 – 0.2) 0.2*(1-0.2) 249 The critical value Zcritical = 20.01 = 2.326348 2.326 P-value = P(Z > ŽSTAT) = P(Z > 0.506979) =1 - P(Z < 0.506979) = 1-0.693915 = 0.306085 20.3061 Conclusion : Since p-value > 0.01 and 2STAT * Zcritical = 2.326348, so We fail to reject Ho at 0.01 level of significance Hence, we can conclude that the population proportion is not significantly greater than 0.2